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99 Percentile Qs Bank for JEE MainMathematicsCircle

The equation of the circle concentric to the circle 2 x 2 + 2 y 2 - 3 x + 6 y + 2 = 0 and having area double the area of this circle is

Options

  1. A8 x 2 + 8 y 2 - 24 x + 48 y - 13 = 0
  2. B16 x 2 + 16 y 2 + 24 x - 48 y - 13 = 0
  3. C16 x 2 + 16 y 2 - 24 x + 48 y - 13 = 0
  4. D8 x 2 + 8 y 2 + 24 x - 48 y - 13 = 0

Correct answer

C. 16 x 2 + 16 y 2 - 24 x + 48 y - 13 = 0

Step-by-step solution

Given the equation of circle can be rewritten as x 2 + y 2 - 3 2 x + 3 y + 1 = 0 Whose center is 3 4 , - 3 2 and radius, r = 9 16 + 9 4 - 1 = 29 16 Area of circle = π r 2 = 29 π 16 ⇒ Area of required circle = 2 × 29 π 16 = 29 π 8 Let R be the radius of the required circle ∴ R 2 = 29 8 Now, the equation of the circle is x - 3 4 2 + y + 3 2 2 = 29 8 ⇒ 16 x 2 + 16 y 2 - 24 x + 48 y - 13 = 0

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