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AP EAMCET20228 Jul 2022Evening ShiftMathematicsCircleActual

The circle x^2+y^2-4 x-8 y+16=0 rolls up along the tangent drawn to it at (2+ 3 , 3) by 2 units. The equation of the circle in the new position is

Options

  1. Ax^2+y^2-6 x-2(4+ 3 ) y+(24+8 3 )=0
  2. Bx^2+y^2-6 x+2(4+ 3 ) y+(24+8 3 )=0
  3. Cx^2+y^2+6 x-2(4+ 3 ) y+(24+8 3 )=0
  4. Dx^2+y^2+6 x+2(4+ 3 ) y+(24+8 3 )=0

Correct answer

A. x^2+y^2-6 x-2(4+ 3 ) y+(24+8 3 )=0

Step-by-step solution

x^2+y^2-4 x-8 y+16=0 C (2,4) aligned & m_ CP = 4-3 2-2- 3 =- 1 3 & m_ CP m_ CC ^ =-1 aligned aligned & m_ CC = 3 & = 3 = 60^ & =60^ & CC ^ =2 aligned Then, C^ (2+2 60^ , 4+2 60^ ) C^ (3,4+ 3 )C^ P^ =2 Equation of new circle : aligned & (x-3)^2+(y-4- 3 )^2=2^2 & x^2+y^2-6 x-2(4+ 3 ) y+9+(4+ 3 )^2=4 & x^2+y^2-6 x-2(4+ 3 ) y+(24+8 3 )=0 aligned

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