If $2 x + y + k = 0$ is a normal to the parabola $y^{2} = - 16 x$ , then find the value of $k$ .

48

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

24

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

12

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

- 48

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

Open in App

Solution

The correct option is A $48$
Equation of normal to the parabola is given by,
$y + t x = 2 a t + a t^{3}$
Here $a = - 4$
$y + t x = - 8 t - 4 t^{3} . . . . (1)$
Now comparing this line to the given line $2 x + y + k = 0$
we get $t = 2$
$\Rightarrow k = 8 t + 4 t^{3} = 8 \times 2 + 4 \times 2^{3} = 48$

Suggest Corrections

Similar questions

2 x + y + k = 0

y^{2} + 8 x = 0

k =

x - 3 = t^{2},

y = 4 t .

x - 3 = t^{2}, y = 4 t

y^{2} = 4 x

y = x + k

y^{2} = 4 x

k

Join BYJU'S Learning Program