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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

If the length of the tangent from any point on the circle x - 3 2 + y + 2 2 = 5 r 2 to the circle x - 3 2 + y + 2 2 = r 2 is 16 units, then the area between the two circles in sq. units is

Options

  1. A32 π
  2. B4 π
  3. C8 π
  4. D256 π

Correct answer

D. 256 π

Step-by-step solution

Let point P ( x 1 ,   y 1 ) be any point on the circle, therefore it satisfies the circle x 1 - 3 2 + y 1 + 2 2 = 5 r 2 . . . . ( i ) The length of the tangent drawn from point P ( x 1 , y 1 ) to the circle x - 3 2 + y + 2 2 = r 2 is S 1 = x 1 - 3 2 + y 1 + 2 2 - r 2 = 5 r 2 - r 2 [from Eq. ( i ) ] = 2 r Given that length of tangent is 16 units ⇒     16 = 2 r     ⇒     r = 8 units ∴ The area between two circles is represented by shaded portion So, area = π (

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