Question 1.
Find the length of the transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices, and the length of the latus rectum of the hyperbolae.
⇒ b = 4 and a = 5
Length of transverse axis = 2b = 2(4) = 8
Length of conjugate axis = 2a = 2(5) = 10
Co-ordinates of vertices are B(0, b) and B’ (0, -b)
i.e., B(0, 4) and B'(0, -4)
We know that
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 5 word image 18221 5](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-5.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 6 word image 18221 6](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-6.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 7 word image 18221 7](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-7.jpeg)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 8 word image 18221 8](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-8.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 9 word image 18221 9](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-9.jpeg)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 10 word image 18221 10](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-10.png)
Length of transverse axis = 2b = 2(5) = 10
Length of conjugate axis = 2a = 2(3) = 6
Co-ordinates of vertices are B(0, b) and B’ (0, -b),
i.e., B(0, 5) and B’ (0, -5)
We know that
⇒ b = 5 and a = 12
Length of transverse axis = 2b = 2(5) = 10
Length of conjugate axis = 2a = 2(12) = 24
Co-ordinates of vertices are B(0, b) and B’ (0, -b),
i.e., B(0, 5) and B’ (0, -5)
We know that
⇒ a = 10 and b = 5
Length of transverse axis = 2a = 2(10) = 20
Length of conjugate axis = 2b = 2(5) = 10
We know that
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 17 word image 18221 17](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-17.png)
Question 2.
Find the equation of the hyperbola with centre at the origin, length of the conjugate axis as 10, and one of the foci as (-7, 0).
Solution:
Question 3.
Question 4.
Solution:
Let e be the eccentricity of a hyperbola
Question 5.
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 24 word image 18221 25](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-25.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 25 word image 18221 26](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-26.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 26 Maharashtra Board 11th Maths Solutions Chapter 7 Conic Sections Ex 7.3 Q5 (iii)](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/maharashtra-board-11th-maths-solutions-chapter-7-c-14.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 27 word image 18221 28](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-28.jpeg)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 28 word image 18221 29](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-29.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 29 word image 18221 30](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-30.jpeg)
(v) Let the required equation of hyperbola be
The hyperbola passes through the points (6, 9) and (3, 0).
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 32 word image 18221 33](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-33.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 33 word image 18221 34](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-34.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 34 word image 18221 35](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-35.png)
![Maharashtra Board Class 11 Maths Part 1 Chapter 7 Conic Sections Ex 7.3 Solution 35 word image 18221 36](https://mhboardsolutions.xyz/wp-content/uploads/2022/02/word-image-18221-36.png)
Question 6.
Solution:
Question 7.
Question 8.
Alternate method:
Question 9.
Question 10.