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AP EAMCET202125 Aug 2021Evening ShiftMathematicsCircleActual

The locus of the centers of the circles that are passing through the intersection of the circles x^2+y^2=1 and x^2+y^2-2 x+y=0 is

Options

  1. Aa line whose equation is x + 2 y = 0.
  2. Ba circle.
  3. Ca parabola.
  4. Da line whose equation is 2 x − y = 0.

Correct answer

A. a line whose equation is x + 2 y = 0.

Step-by-step solution

Equation of the circles passing through the intersection of the circles x^2+y^2=1 and aligned & x^2+y^2-2 x+y=0 is & (x^2+y^2-1 )+k (x^2+y^2-2 x+y )=0 & x^2+y^2- ( 2 k k+1 ) x+ ( k k+1 ) y-1=0 aligned On comparing with general form gathered x^2+y^2+2 g x+2 f y+c=0 g= -k k+1 , f= k 2(k+1) and c=-1 Centre =(-g,-f)= ( k k+1 , -k 2(k+1) ) If x= k k+1 and y= -k 2(k+1) x+2 y=0 gathered

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