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  4. If the normal to the parabola y2=4 ax at the point with parameter t1, cuts the parabola again at the point with parameter t2, then

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Q. If the normal to the parabola $y^2=4 ax$ at the point with parameter $t_1$, cuts the parabola again at the point with parameter $t_2$, then

Conic Sections

Solution:

$t_2=-\left(t_1+\frac{2}{t_1}\right) ; t_2^2=\left(\frac{2}{t_1}+t_1\right)^2=\left(\frac{2}{t_1}-t_1\right)^2+8 \Rightarrow \quad t_2^2 \geq 8$