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NTA Abhyas JEE Main2020MathematicsCirclePractice

From the point A 0,3 on the circle x 2 + 9 x + y - 3 2 = 0 , a chord A B is drawn and extended to a point M such that A M = 2 A B ( B lies between A & M ). The locus of the point M is

Options

  1. Ax 2 + 18 x + y 2 = 0
  2. Bx 2 + 18 x + y - 3 2 = 0
  3. Cx - 3 2 + 18 x + y 2 = 0
  4. Dx 2 + 8 x + 18 - y 2 = 0

Correct answer

B. x 2 + 18 x + y - 3 2 = 0

Step-by-step solution

Let, point M = h , k , then B = h + 0 2 , k + 3 2 which lies on the given circle ⇒ h 2 2 + 9 h 2 + k + 3 2 - 3 2 = 0 ⇒ h 2 + 18 h + k - 3 2 = 0 ⇒ x 2 + 18 x + y - 3 2 = 0

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