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JEE Main20208 Jan 2020Evening ShiftMathematicsHyperbolaActual

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

Options

  1. A3 x + 4 y = 94
  2. B2 x + 5 y = 100
  3. Cx + 2 y = 42
  4. Dx + 3 y = 58

Correct answer

B. 2 x + 5 y = 100

Step-by-step solution

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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