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AP EAMCET201923 Apr 2019Morning ShiftMathematicsCircleActual

A circle (S ) of radius 2 units lies in the first quadrant and touches both the coordinate axes. The equation of the circle with centre at ((6,5) ) and touching the circle (S ) externally is

Options

  1. A(x^2+y^2-12 x-10 y+12=0 )
  2. B(x^2+y^2-12 x-10 y-20=0 )
  3. C(x^2+y^2-12 x-10 y+25=0 )
  4. D(x^2+y^2-12 x-10 y+52=0 )

Correct answer

D. (x^2+y^2-12 x-10 y+52=0 )

Step-by-step solution

From figure Centre of given circle ( (C₁ )=(2,2) ) radius (=2 ) units Centre of required circle ( (C₂ )=(6,5) ) ( array rlr C₁ C₂ & =r+2 ( from figure) & & r & =r+2 array ) ( ) Required equation of circle having centre at ((6,5) ) and (r=3 ) is ( aligned (x-6)^2+(y-5)^2 & =3^2 x^2+y^2-12 x-10 y+52 & =0 aligned ) ( ) Hence, answer is (d).

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