Asymptotes of a rectangular hyperbola $2 x^{2} + 3 x y - 2 y^{2} - 6 x + 13 y - 36 = 0$ are $x + 2 y - 5 = 0$ and $a x + b y + c = 0 (a > 0)$ The ascending order of $a, b, c$ is :

b, a, c

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a, b, c

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c, a, b

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b, c, a

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Solution

The correct option is C $b, a, c$
$(x + 2 y - 5) (a x + b y + c) = 0$
$a x^{2} + 2 a y x - 5 a x + b x y + 2 b y^{2} - 5 b y + c x + 2 c y - 5 c$
$- 5 c + a x^{2} + x y (2 a + b) + 2 b y^{2} + x (c - 5 a) + y (2 c - 5 b)$ -----(1)
$2 x^{2} + 3 x y - 2 y^{2} - 6 x + 13 y - 36 = 0$ ------(2)
Comparing (1) & (2) we get,
$a = 2, b = 1$
$c - 5 a = - 6$
$c = 4$

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