The locus of the middle points of chords of the circle `x^(2)+y^(2)=25` which are parallel to the line `x-2y+3=0`, is

Options

A. x+2y=0
B. 2x+y=0
C. x-2y=0
D. 2x-y=0

Answer

B

Explanation

Let (h,k) be the mid-point of a chord of the circle `x^(2)+y^(2)=25`. Then, equation of the chord is
`hx+ky-25=h^(2)+k^(2)-25rArr hx + ky = h^(2)+k^(2)`
If this is parallel to `x-2y+3=0`, then
`-(1)/(k)=(1)/(2)rArr 2h + k=0`
So, the locus of (h, k) is 2x+y=0