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AP EAMCET202421 May 2024Evening ShiftMathematicsCircleActual

The equation of a circle which touches the straight lines x+y=2, x-y=2 and also touches the circle x^2+y^2=1 is

Options

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

Correct answer

D. (x- 2 )^2+y^2-3 = 2 2

Step-by-step solution

Let r be the radius of required circle. aligned & In Q^ Q P, 45^ O^ Q O^ P 1 2 = r O^ P O^ P=r 2 & O P=2 O R+R O^ +O^ P=2 & 1+r+ 2 r=2 r= 1 2 +1 =( 2 -1) & Centre (1+r, 0)=( 2 , 0) aligned Equation of the required circle is aligned & (x- 2 )^2+(y-0)^2=( 2 -1)^2 & (x- 2 )^2+y^2=3-2 2 aligned

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