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  4. The equation of a tangent to the parabola y2 = 8x is y=x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

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Q. The equation of a tangent to the parabola $y^2 = 8x $ is $y=x + 2.$ The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

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Solution:

$y=mx+\frac{a}{m} $ is a tangent for all values of m where $a = 2$.
For $m = 1, y = x + 2 $
$\therefore $ the equation of the tangent $\bot$ to the given tangent is $y = - x - 2$.
The reqd. point is the point of intersection of these tangents i.e., $\left(- 2, 0\right)$
[ $\because$ perpendicular tangents to a parabola meet on the directrix $x + 2 = 0$]