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Position of a Point W.R.T Ellipse

Find the poin...

Question

Find the point on the curve $y^{2} = 4 x,$ the tangent at which is parallel to the st. line $y = 2 x + 4$

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Solution

$y = 2 x + 4$
Slope $= 2$
$2 y . \frac{d y}{d x} = 4$
$2 y \times 2 = 4$
$y = 1$
$y^{2} = 4 x$
$1 = 4 x$
$x = \frac{1}{4}$
So, $(\frac{1}{4}, 1)$

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