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Find the locus of the points of intersection of the mutually perpendicular tangents to a parabola?

$\begin{array}{1 1}(a)\;h+a=0\\(b)\;h+2a=0\\(c)\;h=a\\(d)\;\text{None of these}\end{array}$

1 Answer

Equation of tangents at point $'t_1'$ and $'t_2'$ are
Slope of tangents is $\large\frac{1}{t_1}$ & $\large\frac{1}{t_2}$ respectively.
Hence $\large\frac{1}{t_1}\times \large\frac{1}{t_2} $$=-1
Now $h=at_1t_2$
$\Rightarrow h+a=0$
Hence (a) is the correct answer.
answered Feb 6, 2014 by sreemathi.v

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