Mathematics - Parabola Question with Solution | TestHub

The directrix must touch the circle $x^2+y^2=2r^2$

$$\therefore \sqrt{2}r=2r=\sqrt{2}.$$

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\end{center} Let ON be the minimum distance line of parabola from circle $\mathrm{N}\equiv \left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\equiv \left({\mathrm{t}}^2+3,2\mathrm{t}+4\right)$ ON must be normal to circle as well as parabola.

$$\frac{2t+4}{t^2+3}=-t$$

$2\mathrm{t}+4=-{\mathrm{t}}^3-3\mathrm{t}{\mathrm{t}}^3+5\mathrm{t}+4=0$ $\left({\mathrm{x}}_1+2\right)\left({\mathrm{y}}_1-4\right)=\left({\mathrm{t}}^2+5\right)2\mathrm{t}=2\left({\mathrm{t}}^3+5\mathrm{t}\right)=-8$.