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JEE Main202225 Jun 2022Evening ShiftMathematicsCircleActual

A circle touches both the y -axis and the line x + y = 0 . Then the locus of its center

Options

  1. Ay = 2 x
  2. Bx = 2 y ..
  3. Cy 2 - x 2 = 2 x y
  4. Dx 2 − y 2 = 2 x y

Correct answer

D. x 2 − y 2 = 2 x y

Step-by-step solution

Plotting the diagram of given data we have, Now to find locus, let centre be h , k . According to question O M = O N distance ⇒ h = h + k 2 squaring both sides we get ⇒ 2 h 2 = h + k 2 ⇒ 2 h 2 = h 2 + k 2 + 2 h k Replacing h with x & k with y we get 2 x 2 = x 2 + y 2 + 2 x y ⇒ x 2 − y 2 = 2 x y

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