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AP EAMCET202022 Sep 2020Morning ShiftMathematicsCircleActual

Find the equation of a circle with radius 5 units and touching the circle x^2+y^2-2 x-4 y-20=0 at the point (5,5) .

Options

  1. Ax^2+y^2-18 x-16 y+120=0
  2. Bx^2+y^2+18 x+16 y-120=0
  3. Cx^2+y^2-18 x+16 y-120=0
  4. Dx^2+y^2+18 x+16 y+120=0

Correct answer

A. x^2+y^2-18 x-16 y+120=0

Step-by-step solution

Equation of given circle array rlrl x^2+y^2-2 x-4 y-20 & =0 & & (x-1)^2+(y-2)^2 & =25 array Having centre C₁(1,2) and radius 5 units. Another circle touches the circle (i) at point (5,5) having radius 5 units, so centre ' C₂ ' of the second circle is collinear with C₁ and point (5,5) is the mid-point of C₁ C₂ , so C₂(9,8) . So, equation of the second circle is aligned (x-9)^2+(y-8)^2 & =25 x^2+y^2-18 x-16 y+120 & =0 aligned

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