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AP EAMCET202018 Sep 2020Evening ShiftMathematicsCircleActual

The equation of the circle with centre ((2,3) ) and touching the line (3 x-4 y+1=0 ) is

Options

  1. A(x^2+y^2+4 x+4 y+12=0 )
  2. B(x^2+y^2-4 x-6 y-14=0 )
  3. C(x^2+y^2-4 x-6 y+14=0 )
  4. D(x^2+y^2-4 x-6 y+12=0 )

Correct answer

D. (x^2+y^2-4 x-6 y+12=0 )

Step-by-step solution

Centre (c=(2,3) ) radius (= ) Perpendicular distance from centre ((2,3) ) to the line (3 x-4 y+1=0 ) ( aligned & r= |3(2)-4(3)+1| 3^2+(-4)^2 = |7-12| 25 & r= 5 5 =1 aligned ) Equation of circle is ( aligned (x-2)^2+(y-3)^2 & =(1)^2 x^2+4-4 x+y^2+9-6 y & =1 x^2+y^2-4 x-6 y+13-1 & =0 x^2+y^2-4 x-6 y+12 & =0 aligned ) Hence, option (d) is correct.

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