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JEE Main20249 Apr 2024Morning ShiftMathematicsCircleActual

Let a circle passing through (2,0) have its centre at the point (h, k) . Let (x_c, y_c ) be the point of intersection of the lines 3 x+5 y=1 and (2+c) x+5 c^2 y=1 . If h = _ c 1 x_ c and k = _ c 1 y_ c , then the equation of the circle is :

Options

  1. A25 x^2+25 y^2-2 x+2 y-60=0
  2. B5 x^2+5 y^2-4 x+2 y-12=0
  3. C5 x^2+5 y^2-4 x-2 y-12=0
  4. D25 x^2+25 y^2-20 x+2 y-60=0

Correct answer

D. 25 x^2+25 y^2-20 x+2 y-60=0

Step-by-step solution

aligned & (2+c) x+5 c^2 ( 1-3 x 5 )=1 & x= 1-c^2 2+c-3 c^2 , y= 1-3 x 5 = c-1 5 (2+c-3 c^2 ) & h= _ c 1 (1-c)(1+c) (1-c)(2+3 c) = 2 5 & K= _ c 1 c-1 -5(c-1)(3 c+2) =- 1 25 & Centre ( 2 25 ,- 1 25 ) aligned aligned & r= (2- 2 5 )^2+ (0- 1 25 )^2 = 64 25 + 1 625 & r= 161 25 & (x- 2 5 )^2+ (y+ 1 25 )^2= 161 125 & 25 x^2+25 y^2-20 x+2 y-60=0 aligned

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