The angle between the tangents drawn from the point $(- a, 2 a)$ to $y^{2} = 4 a x$ is

\frac{π}{4}

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

\frac{π}{2}

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

\frac{π}{3}

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

\frac{π}{6}

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

Open in App

Solution

The correct option is B $\frac{π}{2}$
$(- a, 2 a)$
$y^{2} = 4 a x$

$y = m x + \frac{a}{m}$ is tangent to parabola $y^{2} = 4 a x$

it is pass through point $(- a, 2 a)$

$2 a = \frac{- m a}{1} + \frac{a}{m}$

$m^{2} a + 2 a m - a = 0$

$m^{2} + 2 m - 1 = 0$

$m = - 1 \pm \sqrt{2}$

$m_{1} = \sqrt{2} - 1, m_{2} = - \sqrt{2} - 1$

$m_{1} + m_{2} = 2$

$m_{1} . m_{2} = - 1$

$m_{1} - m_{2} = 2 \sqrt{2}$

$t a n θ = | \frac{m_{1} - m_{2}}{1 + m_{1} . m_{2}} |$

$t a n θ = \frac{2 \sqrt{2}}{0} = \infty$

$θ = \frac{π}{2}$

Suggest Corrections

Similar questions

The angle between the tangents drawn from the point (1, 4) to the parabola $y^{2}$ = 4x is

x^{2} + y^{2} = 41

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

(a, a)

x^{2} + y^{2} - 2 x - 2 y - 6 = 0

(\frac{π}{3}, π)

a

y = x^{2} - 5 x + 6

The angle between the tangents to the curve $y^{2} = 2 a x$ at the points where $x = \frac{a}{2}$ , is

Join BYJU'S Learning Program