NCERT Solutions for Class 11 Maths Chapter 11 – Conic Sections Ex 11.4
Page No 262:
Question 1:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_42610b97.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_42610b97.gif)
Answer:
The given equation is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_414f24f2.gif)
On comparing this equation with the standard equation of hyperbola i.e.,
, we obtain a = 4 and b = 3.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_3a003c40.gif)
Therefore,
The coordinates of the foci are (±5, 0).
The coordinates of the vertices are (±4, 0).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_17815d06.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_3818a1a6.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4830/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_3818a1a6.gif)
Question 2:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_31f97c09.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_31f97c09.gif)
Answer:
The given equation is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_11ebf286.gif)
On comparing this equation with the standard equation of hyperbola i.e.,
, we obtain a = 3 and
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m73892847.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_7f2f98f7.gif)
Therefore,
The coordinates of the foci are (0, ±6).
The coordinates of the vertices are (0, ±3).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m7c9be18d.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m37d73f3d.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4832/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m37d73f3d.gif)
Question 3:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y2 – 4x2 = 36
Answer:
The given equation is 9y2 – 4x2 = 36.
It can be written as
9y2 – 4x2 = 36
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m718e4008.gif)
On comparing equation (1) with the standard equation of hyperbola i.e.,
, we obtain a = 2 and b = 3.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1f211a6e.gif)
Therefore,
The coordinates of the foci are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_11e4896a.gif)
The coordinates of the vertices are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_7efdea5e.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m55cc08b2.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_42d4563b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4835/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_42d4563b.gif)
Question 4:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 – 9y2 = 576
Answer:
The given equation is 16x2 – 9y2 = 576.
It can be written as
16x2 – 9y2 = 576
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m509d93f4.gif)
On comparing equation (1) with the standard equation of hyperbola i.e.,
, we obtain a = 6 and b = 8.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_28c9ab25.gif)
Therefore,
The coordinates of the foci are (±10, 0).
The coordinates of the vertices are (±6, 0).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_55ec5792.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_75193562.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4836/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_75193562.gif)
Question 5:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y2 – 9x2 = 36
Answer:
The given equation is 5y2 – 9x2 = 36.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m17bd206f.gif)
On comparing equation (1) with the standard equation of hyperbola i.e.,
, we obtain a =
and b = 2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_md38009f.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1a4da293.gif)
Therefore, the coordinates of the foci are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_37cecc83.gif)
The coordinates of the vertices are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_7b4d72ee.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m209a3f40.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1bc2151f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4837/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1bc2151f.gif)
Question 6:
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 – 16x2 = 784
Answer:
The given equation is 49y2 – 16x2 = 784.
It can be written as 49y2 – 16x2 = 784
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m2b8a10f.gif)
On comparing equation (1) with the standard equation of hyperbola i.e.,
, we obtain a = 4 and b = 7.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_53a5dc98.gif)
Therefore,
The coordinates of the foci are
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_240316c5.gif)
The coordinates of the vertices are (0, ±4).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_135f67fc.gif)
Length of latus rectum![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_ma313c9b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4838/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_ma313c9b.gif)
Question 7:
Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)
Answer:
Vertices (±2, 0), foci (±3, 0)
Here, the vertices are on the x-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4839/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
Since the vertices are (±2, 0), a = 2.
Since the foci are (±3, 0), c = 3.
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4839/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_3e4f7397.gif)
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4839/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1419729.gif)
Question 8:
Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)
Answer:
Vertices (0, ±5), foci (0, ±8)
Here, the vertices are on the y-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4840/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
Since the vertices are (0, ±5), a = 5.
Since the foci are (0, ±8), c = 8.
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4840/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_14432639.gif)
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4840/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_710bfc03.gif)
Question 9:
Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)
Answer:
Vertices (0, ±3), foci (0, ±5)
Here, the vertices are on the y-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4842/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
Since the vertices are (0, ±3), a = 3.
Since the foci are (0, ±5), c = 5.
We know that a2 + b2 = c2.
∴32 + b2 = 52
⇒ b2 = 25 – 9 = 16
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4842/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_58b45b65.gif)
Question 10:
Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.
Answer:
Foci (±5, 0), the transverse axis is of length 8.
Here, the foci are on the x-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4843/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
Since the foci are (±5, 0), c = 5.
Since the length of the transverse axis is 8, 2a = 8 ⇒ a = 4.
We know that a2 + b2 = c2.
∴42 + b2 = 52
⇒ b2 = 25 – 16 = 9
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4843/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m511f9386.gif)
Question 11:
Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.
Answer:
Foci (0, ±13), the conjugate axis is of length 24.
Here, the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4844/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
Since the foci are (0, ±13), c = 13.
Since the length of the conjugate axis is 24, 2b = 24 ⇒ b = 12.
We know that a2 + b2 = c2.
∴a2 + 122 = 132
⇒ a2 = 169 – 144 = 25
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4844/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1b9c159e.gif)
Question 12:
Find the equation of the hyperbola satisfying the give conditions: Foci
, the latus rectum is of length 8.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1b661338.gif)
Answer:
Foci
, the latus rectum is of length 8.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1b661338.gif)
Here, the foci are on the x-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
Since the foci are
, c =
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_1b661338.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_6feae8dd.gif)
Length of latus rectum = 8
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_180fe2ef.gif)
We know that a2 + b2 = c2.
∴a2 + 4a = 45
⇒ a2 + 4a – 45 = 0
⇒ a2 + 9a – 5a – 45 = 0
⇒ (a + 9) (a – 5) = 0
⇒ a = –9, 5
Since a is non-negative, a = 5.
∴b2 = 4a = 4 × 5 = 20
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4845/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_18e41b56.gif)
Question 13:
Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12
Answer:
Foci (±4, 0), the latus rectum is of length 12.
Here, the foci are on the x-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4846/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
Since the foci are (±4, 0), c = 4.
Length of latus rectum = 12
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4846/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m76c7b892.gif)
We know that a2 + b2 = c2.
∴a2 + 6a = 16
⇒ a2 + 6a – 16 = 0
⇒ a2 + 8a – 2a – 16 = 0
⇒ (a + 8) (a – 2) = 0
⇒ a = –8, 2
Since a is non-negative, a = 2.
∴b2 = 6a = 6 × 2 = 12
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4846/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m3604f7d3.gif)
Question 14:
Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
Answer:
Vertices (±7, 0), ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
Here, the vertices are on the x-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_452a20d9.gif)
Since the vertices are (±7, 0), a = 7.
It is given that ![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_4d4605ae.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_741f8acc.gif)
We know that a2 + b2 = c2.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_21dee499.gif)
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4847/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_36974c71.gif)
Question 15:
Find the equation of the hyperbola satisfying the give conditions: Foci
, passing through (2, 3)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m7f61218.gif)
Answer:
Foci
, passing through (2, 3)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m7f61218.gif)
Here, the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m515f458b.gif)
Since the foci are
, c =
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m7f61218.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m1829d81a.gif)
We know that a2 + b2 = c2.
∴ a2 + b2 = 10
⇒ b2 = 10 – a2 … (1)
Since the hyperbola passes through point (2, 3),
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_14845639.gif)
From equations (1) and (2), we obtain
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_580a5c86.gif)
In hyperbola, c > a, i.e., c2 > a2
∴ a2 = 5
⇒ b2 = 10 – a2 = 10 – 5 = 5
Thus, the equation of the hyperbola is
.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/11/11/171/4848/NS_15-10-08_KHushboo_11_Math_Chapter11.1_15_SU_SNK_html_m7f01a2ea.gif)