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AP EAMCET2012MathematicsCircle

If the line x+3 y=0 is the tangent at (0,0) to the circle of radius 1 , then the centre of one such circle is

Options

  1. A(3,0)
  2. B( -1 10 , 3 10 )
  3. C( 3 10 , -3 10 )
  4. D( 1 10 , 3 10 )

Correct answer

D. ( 1 10 , 3 10 )

Step-by-step solution

Given line is x+3 y=0 . Slope of a line =- 1 3 Let the centres of circle be (+g,+f) . We know that, the perpendicular drawn from the centre to the tangent is equal to radius. Since perpendicular distance from (g, f) to the line is 1 . Since perpendicular distance from (g, f) to the line is 1 . array ll & +g+3 f 1^2+3^2 =1 & +g+3 f 10 =1 array Taking option (d) i.e., centre = ( 1 10 , 3 10 ) + 1 10 +3 3 10 10 = 10 10 =1 (true)

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