If line y-2x-14 is tangent toy2-4ax then a is equal to

Given : y=2x+14 is tangent to y^2=4ax here, slope of tangent =2 nbsp; Consider y^2=4ax if slope of tangent is m then nbsp; nbsp;point on parabola will be ...

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If line y=2x+...

Question

$If line y = 2 x + \frac{1}{4} is tangent to$
$y^{2} = 4 a x then a is equal to$

\frac{1}{2}

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None of the above

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Solution

The correct option is A $\frac{1}{2}$
Given : $y = 2 x + \frac{1}{4}$ is tangent to
$y^{2} = 4 a x$
here, slope of tangent $= 2$

Consider $y^{2} = 4 a x$
if slope of tangent is $m$ then point on parabola will be $(\frac{a}{m^{2}}, \frac{2 a}{m})$

So point on parabola is $(\frac{a}{4}, a)$
This point will satisfy the equation of tangent , hence
$\Rightarrow a = 2 (\frac{a}{4}) + \frac{1}{4}$
$\Rightarrow a = \frac{1}{2}$
Hence, Option A is correct answer

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If line y=2x+14 is tangent to y2=4ax then a is equal to

$If line y = 2 x + \frac{1}{4} is tangent to$
$y^{2} = 4 a x then a is equal to$