Mathematics - Parabola Question with Solution | TestHub

For perpendicular chords from the vertex, $t_1{t}_2=-4$. With $A=\left(a{t}_1^2,2a{t}_1\right),B=$ $\left(a{t}_2^2,2a{t}_2\right)$, midpoints P and Q, the centre $C=(h,k)$ of the circle through O, P, Q satisfies $h=\frac{a}{4}\left(t_1^2+t_2^2\right),k=\frac{a}{2}\left(t_1+t_2\right)$. Then $k^2=\frac{a^2}{4}\left(t_1^2+t_2^2+2t_1{t}_2\right)=ah-2a^2$, so $y^2=a(x-2a)$.