Question

The centre of the hyperbola $9x^{2} - 36x - 16y^{2} + 96y - 252 = 0$ is

• A. (2, 3)
• B. (– 2, – 3)
• C. (–2, 3)
• D. (2, – 3)

Answer 1

Answer: (A)

(2, 3)

Answer 2

Here $a = 9,$ $b = - 16,$ $h = 0$, $g = - 18$, $f = 48$ , $c = - 252$

Centre of hyperbola = $\left( \frac{hf - bg}{ab - h^{2}},\frac{gh - af}{ab - h^{2}} \right)$ =

$\left( \frac{(0)(48) - ( - 16)( - 18)}{(9)( - 16) - 0},\frac{( - 18)(0) - (9)(48)}{(9)( - 16) - 0} \right)$ = (2, 3)