Question

Find the locus of the middle points of chords of the circle $x^2+y^2=a^2$ which pass through the fixed point $(h,k)$.

Answer 1

Let $(x_1,y_1)$ be the middle point of chord
$x{x}_1+y{y}_1=x_1^2+y_1^2$
Since it passes through $(h,k)$
$h{x}_1+k{y}_1=x_1^2+y_1^2$
Now replace $x_1$ by $x$ and $y_1$ by $y$
$hx+ky=x^2+y^2$