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 ...

You visited us 74 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Factorise $1 - (2 x - 3 y)^{2}$

f (x) = \frac{1 + 2 x}{1 - 2 x} + \frac{1 - 2 x}{1 + 2 x}

Find

f (1)

Evaluate $\int \frac{1}{(1 - x^{2}) \sqrt{1 + x^{2}}} d x$

$(4 x^{2} + 4 x - 3) = ?$
(a) $(2 x - 1) (2 x - 3)$
(b) $(2 x + 1) (2 x - 3)$
(c) $(2 x + 3) (2 x - 1)$
(d) none of these

Q. If

2^{x} + 2^{y} = 2^{x + y}

, then

\frac{d y}{d x}

is equal to

Join BYJU'S Learning Program

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

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