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AP EAMCET202017 Sep 2020Evening ShiftMathematicsCircleActual

The equations of tangents to the circle (x^2+y^2=10 ) from the point ((4,-2) ) are

Options

  1. A(x+y=2,3 x+2 y=16 )
  2. B(5 x+y=18,3 x-y=4 )
  3. C(3 x+y=10, x-3 y=10 )
  4. D(5 x-y=4, x+y=0 )

Correct answer

C. (3 x+y=10, x-3 y=10 )

Step-by-step solution

For a tangent, length of perpendicular from origin (= ) radius. So we check distance from ((0,0) ) and for any tangent it must be ( 10 ). For (3 x+y=10 ) and (x-3 y=10 ), Distance of ((0,0) ) from line (3 x+y=10 ) is, (d= | 3 0+0-10 3^2+1^2 |= | 10 10 |= 10 ) Also from (x-3 y=10 ), (d= | 0-3 0-10 3^2+1^2 |= 10 ) So, option (c) is correct.

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