**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

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

**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.**

(v) Let the required equation of hyperbola be

The hyperbola passes through the points (6, 9) and (3, 0).

**Question 6.Solution:**

**Question 7.**

**Question 8.**

Alternate method:

**Question 9.**

**Question 10.**