Mathematics - Parabola Question with Solution | TestHub

Let the other end of diameter is $(\mathrm{h},\mathrm{k})$ then equation of circle is $$(x-h)(x-p)+(y-k)(y-q)=0$$ Put $y=0$, since $x$-axis touches the circle $$\begin{array}{rl}& \Rightarrow x^2-(h+p)x+(hp+kq)=0\Rightarrow (h+p{)}^2=4(hp+kq)(D=0)\\ & \Rightarrow (x-p{)}^2=4qy.\end{array}$$