If equation of hyperbola passing through $ (-2,1) $ and having asymptotes $ 2 x+y+5=0 $ and $ x-6 y+3=0 $ is $ a x^{2}+b y^{2}+2 h x y+2 g x+2 f y+c=0 $, then value of $ c $ is

Question

If equation of hyperbola passing through $ (-2,1) $ and having asymptotes $ 2 x+y+5=0 $ and $ x-6 y+3=0 $ is $ a x^{2}+b y^{2}+2 h x y+2 g x+2 f y+c=0 $, then value of $ c $ is,

MARKS App · Accepted Answer

Equation of hyperbola will be 2 x + y + 5 x - 6 y + 3 + λ = 0 It passes through ( - 2 , 1 ) , so - 4 + 1 + 5 - 2 - 6 + 3 + λ = 0 ⇒ λ = 10 Hence, equation of hyperbola wiil be 2 x 2 - 6 y 2 - 11 x y + 6 x - 10 y + 25 = 0 On comparing with a x 2 + b y 2 + 2 h x y + 2 g x + 2 f y + c = 0 , we get, c = 25

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