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AP EAMCET202018 Sep 2020Evening ShiftMathematicsCircleActual

Find the minimum radius of the circle which is orthogonal to both the circles (x^2+y^2+4 x+3=0 ) and (x^2+y^2-12 x+35=0 ).

Options

  1. A1
  2. B4
  3. C( 17 )
  4. D( 15 )

Correct answer

D. ( 15 )

Step-by-step solution

Centre of circle cuts the circles ( aligned S₁: x^2+y^2+4 x+3 & =0 S₂: x^2+y^2-12 x+35 & =0 aligned ) Radical Axis is (S₁-S₂=0 x=2 ) and ((2,0) ) lies on the line segment joining centres of circles (S₁ ) and (S₂ ) Minimum radius (= ) length of tangent from ((2,0) ) ( to circle aligned S₁ & =0 (or) S₂=0 & = 4+8+3 = 15 aligned ) Hence, option (d) is correct.

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