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Perpendicular Distance of a Point from a Line

If the tangen...

Question

If the tangents at $t_{1}$ and $t_{2}$ to a parabola are perpendicular then the value of $| (t_{1} + t_{2})^{2} - (t_{1} - t_{2})^{2} |$ is

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Solution

If the tangents at $t_{1}$ and $t_{2}$ to a parabola are perpendicular then $t_{1} \cdot t_{2} = - 1$
$(t_{1} + t_{2})^{2} - (t_{1} - t_{2})^{2} = 4 t_{1} \cdot t_{2} = 4 (- 1) = - 4$
$\Rightarrow | (t_{1} + t_{2})^{2} - (t_{1} - t_{2})^{2} | = | - 4 | = 4$

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