Through a fixed point (h,k), secant are drawn to the circle `x^(2)+y^(2)=r^(2)`. Show that the locus of the midpoints of the secants by the circle is `x^(2)+y^(2)=hx+ky`.

Options

A. `2(x^(2)+y^(2))=hx+ky`
B. `x^(2)+y^(2)=hx+ky`
C. `x^(2)+y^(2)+hx+ky=0`
D. `x^(2)+y^(2)-hx+ky+13=0`

Answer

B

Explanation

Let mid point of the chord be `P(x_(1),y_(1))`
`:.` Equation of chord `S_(1)=T`
`x_(1)^(2)+y_(1)^(2)-a^(2)="xx"_(1)+"yy"_(1)-a^(2)`
This chord passes through (h,k)
`x_(1)^(2)+y_(1)^(2)=hx_(1)+ky_(1)" ":." "` Locus of `P(x_(1),y_(1))` be `x_(1)^(2)+y_(1)^(2)=hx_(1)+ky_(1)`