Question

The locus of the centres of circles passing through the origin and intersecting the fixed circle `x^(2)+y^(2)-5x+3y-1=0` orthogonally is
A. a straight line of slope 3/5
B. a circle
C. a pair of straight lines
D. none of these

Answer 1

Correct Answer - D
Let the circle be
`x^(2)+y^(2)+2gx+2fy+c=0` ...(i)
If passes through the origin and cuts the circle `x^(2)+y^(2)-5x+3y-1=0` orthogonally.
`:. C=0 and , 2(-(5)/(2)g+(3)/(2)f)=c-1rArr -5g+3f=-1`
Hence, the locus of `(-g, -f) ` is `5x-3y=-1`.