Question

Find the centre, vertices, eccentricity and foci of the hyperbola 9x² - 18x - 16y² - 64y + 89 = 0.

Answer 1

The given equation is

which is the conjugate hyperbola of

The centre is (x -1 = 0, y + 2 = 0) = (1,-2) The eccentricity e is given by

16 = 9(e² - 1)  ⇒ e = 5/3 

so that  be = 3(5/3) = 5

The foci is (x - 1 = 0, y + 2 = ±be) which is given by (1,y = -2 ± 5) = (1,3) and (1,-7)