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AP EAMCET202318 May 2023Evening ShiftMathematicsCircleActual

Let C be the centre and A be one end of a diameter of the circle x^2+y^2-2 x-4 y-20=0 . If P is a point on A C such that A divides CP in the ratio 2: 3 , then the locus of P is

Options

  1. Ax^2+y^2-2 x-4 y-205=0
  2. B2 x^2+2 y^2-4 x-8 y-405=0
  3. Cx^2+y^2-2 x-4 y-450=0
  4. D4 x^2+4 y^2-8 x-16 y-605=0

Correct answer

D. 4 x^2+4 y^2-8 x-16 y-605=0

Step-by-step solution

The centre of cirlce x^2+y^2-2 x-4 y-20=0 is C (1,2) A.T. Q A ( x , y )= ( 2 ~h +3 5 , 2 k +6 5 ) Putting the value of x and y in equation (i) aligned & ( 2 h+3 5 )^2+ ( 2 k+6 5 )^2-2 (2 h+3) 5 -4 (2 k+6) 5 -20=0 & 4 h^2+9+12 h+4 k^2+36+24 k-20 h-30-40 k-120 & -500=0 & 4 h^2+4 k^2-8 h-16 k-605=0 & Locus of P is 4 x^2+4 y^2-8 x-16 y-605=0 aligned

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