Question

Two tangents to the parabola y^2=8x meet the tangent at its vertex in

Answer 1

The equation of tangent is x=0

Step-by-step explanation:

Given equation of parabola,

$y^2=8ax$          [ The vertex of the parabola is(0,0)]

Diff. w. r. to x

$2y\frac{dy}{dx} =8$

$\Rightarrow \frac{dy}{dx} =\frac{8}{2y}$

$\Rightarrow \frac{dy}{dx} =\frac{4}{y}$

$\Rightarrow [\frac{dy}{dx}]_{(0,0)} =\frac{4}{0}$

The equation of line passes through the origin is

y=mx [ m is slope of the line]

The equation of tangent is

$y=\frac{4}{0} x$

$\Rightarrow x=0$

Answer 2

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The equation of tangent is x=0