If a hyperbola passes through the point $ P(10,16) $, and it has vertices at $ (\pm 6,0) $, then the equation of the normal to it at $ P $, is.

Question

If a hyperbola passes through the point $ P(10,16) $, and it has vertices at $ (\pm 6,0) $, then the equation of the normal to it at $ P $, is., $ 3 x+4 y=94 $, $ 2 x+5 y=100 $, $ x+2 y=42 $, $ x+3 y=58 $

MARKS App · Accepted Answer

Let the equation of hyperbola is x 2 a 2 - y 2 b 2 = 1 . As, vertex is at ± 6 , 0 , and it passes through 10 , 16 , So, the equation of hyperbola is x 2 36 - y 2 144 = 1 . Equation of normal to the hyperbola at x 1 , y 1 is a 2 x x 1 + b 2 y y 1 = a 2 + b 2 Thus, on putting values, equation of normal is 2 x + 5 y = 100 .

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