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AP EAMCET201825 Apr 2018Morning ShiftMathematicsCircleActual

If the lengths of the tangents drawn from a point P to the three circles x 2 + y 2 - 4 = 0 , x 2 + y 2 - 2 x + 3 y = 0 and x 2 + y 2 + 7 y - 18 = 0 are equal, then the coordinates of P are

Options

  1. A( 2 , 5 )
  2. B( 3 , 4 )
  3. C( 4 , 3 )
  4. D( 5 , 2 )

Correct answer

D. ( 5 , 2 )

Step-by-step solution

Given: S 1 ≡ x 2 + y 2 - 4 = 0 S 2 ≡ x 2 + y 2 - 2 x + 3 y = 0 S 3 ≡ x 2 + y 2 + 7 y - 18 = 0 We know if the length of tangents drawn from an external points to three circles are equal, then that point is the radical centre. First we will find the radical axes which is S 1 - S 2 = 0   or   S 2 - S 3 = 0 We take, S 1 - S 2 = 0 ⇒ 2 x - 3 y - 4 = 0     . . . i And, S 1 - S 3 = 0 - 7 y + 18 - 4 = 0     . . . i i Solving i   &   i i , we get x = 5 &#160

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