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JEE Main202116 Mar 2021Morning ShiftMathematicsHyperbolaActual

The locus of the midpoints of the chord of the circle, x 2 + y 2 = 25 which is tangent to the hyperbola, x 2 9 - y 2 16 = 1 is :

Options

  1. Ax 2 + y 2 2 - 16 x 2 + 9 y 2 = 0
  2. Bx 2 + y 2 2 - 9 x 2 + 144 y 2 = 0
  3. Cx 2 + y 2 2 - 9 x 2 - 16 y 2 = 0
  4. Dx 2 + y 2 2 - 9 x 2 + 16 y 2 = 0

Correct answer

D. x 2 + y 2 2 - 9 x 2 + 16 y 2 = 0

Step-by-step solution

Equation of chord y - k = - h k x - h k y - k 2 = - h x + h 2 h x + k y = h 2 + k 2 y = - h x k + h 2 + k 2 k tangent to x 2 9 - y 2 16 = 1 c 2 = a 2 m 2 - b 2 h 2 + k 2 k 2 = 9 - h k 2 - 16 x 2 + y 2 2 = 9 x 2 - 16 y 2

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