For the parabola $y^{2} = 4 a x$ , the ratio of the sub-tangent to the abcissa is

1 : 1

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

2 : 1

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

x : y

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

$x^{2} : y$

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

Open in App

Solution

The correct option is B
2 : 1

We have, $y^{2} = 4 a x$
$\Rightarrow 2 y \frac{d y}{d x} = 4 a \Rightarrow \frac{d y}{d x} = \frac{2 a}{y} . S u b - t a n g e n t = \frac{y}{d y / d x} = \frac{y}{2 a / y} = \frac{y^{2}}{2 a} = \frac{4 a x}{2 a} = 2 x .$
$∴$ Sub - tangent : Abcissa = 2x : x = 2 : 1,
Hence (b) is the correct answer.

Suggest Corrections

Similar questions

For the parabola $y^{2} = 4 a x$ , the ratio of the sub-tangent to the abcissa is

y^{2} = 16 x

y^{2} = 16 x

y^{2} = 4 a x

Join BYJU'S Learning Program