For the parabola, $y^{2} = 16 x$ , the ratio of the length of subtangent to the abcissa is

1 : 1

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!

x : y

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

Open in App

Solution

The correct option is D $2 : 1$
$y^{2} = 16 x$
$\Rightarrow \frac{d x}{d y} = \frac{y}{8}$
Length of subtangent $= ∣ ∣ ∣ y \frac{d x}{d y} ∣ ∣ ∣ = \frac{y^{2}}{8}$
Ratio of length of subtangent to abscissa $= \frac{\frac{y^{2}}{8}}{x} = \frac{y^{2}}{8 x} = \frac{16 x}{8 x} = \frac{2}{1}$
So, the answer is option (D).

Suggest Corrections

Similar questions

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

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

(3, 5)

x^{2} + x y + y^{2} = 7

(1, - 3)

y^{2} = 4 a x

y^{2} = 4 a x

Join BYJU'S Learning Program