Question

For the hyperbola 9x² - 16y² - 18x + 32y - 151 = 0 , which of the following are true?

(A)   Eccentricity is 5/4

(B)   Foci are (-4,1) and (6,1)

(C)  Centre is (1, -1)

(D)  Length of the latus rectum is 9/2

Answer 1

Correct option  (a)(c)(d)

Explanation :

The given equation is

where X = x - 1, Y = y + 1. Here a² = 16, b² = 9. The eccentricity e is given by

9 = 16(e² = 1+ 9/16 = 25/16

So that

e = 5/4

The centre is given by

(X = 0, Y = 0) = (x - 1= 0, y + 1 = 0) = (1, - 1)

2b²/a = 2(9)/9 = 9/2