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Slope Form of Tangent: Ellipse

lf the tangen...

Question

lf the tangents at $t_{1}$ and $t_{2}$ to a parabola are perpendicular then $(t_{1} + t_{2})^{2} - (t_{1} - t_{2})^{2} =$

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Solution

The correct option is B $- 4$
Let the equation of the tangents be $x - y t_{1} + a {t_{1}}^{2} = 0$ and $x - y t_{2} + a {t_{2}}^{2} = 0$
Since, tangents are perpendicular.
Therefore, $t_{1} t_{2} = - 1$
Now, $(t_{1} + t_{2})^{2} - (t_{1} - t_{2})^{2} = 4 t_{1} t_{2} = - 4$

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