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AP EAMCET · Maths · Circle

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 \((5,5)\).

  1. A \(x^2+y^2-18 x-16 y+120=0\)
  2. B \(x^2+y^2+18 x+16 y-120=0\)
  3. C \(x^2+y^2-18 x+16 y-120=0\)
  4. D \(x^2+y^2+18 x+16 y+120=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x^2+y^2-18 x-16 y+120=0\)

Step-by-step Solution

Detailed explanation

Equation of given circle \[ \begin{array}{rlrl} x^2+y^2-2 x-4 y-20 & =0 \\ \Rightarrow & & (x-1)^2+(y-2)^2 & =25 \end{array} \] Having centre \(C_1(1,2)\) and radius 5 units. \(\because\) Another circle touches the circle (i) at point \((5,5)\) having radius 5 units, so centre '…