First slide

Parabola

Question

Equation of a normal to the parabola $y^{2} = 32 x$ passing through its focus is

Moderate

A

$x = 0$
B

$y = 0$
C

$x + y - 8 = 0$
D

$x - y - 8 = 0$

Solution

Equation of a normal to the parabola is
$y = m x - 2 a m - a m^{3}, 4 a = 32 \Rightarrow a = 8$
which passes through the focus (8, 0)
If $0 = 8 m - 16 m - 8 m^{3} = 0$
$\Rightarrow m^{3} + m = 0 \Rightarrow m (m^{2} + 1) = 0 \Rightarrow m = 0$
and the required equation of the normal is $y = 0 .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App