Find the locus of the midpoint of the chord of the circle $x^2 + y^2=a^2$ which subtends a $90°$ angle at point $(p,q)$ lying inside the circle.
I tried to solve it by taking that let the chord intersect the circle at $(x_1,y_1)$ and $(x_2,y_2)$. Then I found out their slopes and took their product as $-1$. I also tried by taking the lines joining center from chord as perpendicular.
But I couldn't do it. Please tell me a way.