Find equation tangent to parabola $y^{2} = 4 x$ whose intercept on $y - a x i s$ is $2$ .

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Solution

$y^{2} = 4 x$
$y = 2$
$e q^{n}$ of tangent to the parabola $[y^{2} = 4 a x]$ is $y = m x + \frac{a}{m}$
here parabola $e q^{n}$ is $y^{2} = 4 x$
so, a = 1;
So, $e q^{n}$ of tangent is $y = m x + \frac{a}{m}$
$∵ y$ intercept is 2 so tangent passes
through (0,2), so it satisfies $e q^{n}$
of tangent.
$2 = m .0 + \frac{1}{m}$
$m = \frac{1}{2}$
So, $e q^{n}$ of tangent is $y = m x + \frac{a}{m}$
$y = \frac{1}{2} x + 2$
$2 y = x + 4$

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Find equation tangent to parabola y2=4x whose intercept on y−axis is 2.

y2=4xy=2eqn of tangent to the parabola [y2=4ax] is y=mx+amhere parabola eqn is y2=4xso, a = 1;So,eqn of tangent is y=mx+am∵y intercept is 2 so tangent passesthrough (0,2), so it satisfies eqnof tangent.2=m.0+1mm=12So, eqn of tangent is y=mx+amy=12x+22y=x+4

Find equation tangent to parabola $y^{2} = 4 x$ whose intercept on $y - a x i s$ is $2$ .