Question

The length of double ordinate of parabola $y^2=8x$ which subtends an angle ${60}^0$ at vertex in

• A. $4\sqrt{3}$
• B. $8\sqrt{3}$
• C. $16\sqrt{3}$
• D. $324\sqrt{3}$

Answer 1

The correct option is C $16\sqrt{3}$

REF.Image

Que: double ordinate is a perpendicular line to parabola,

$\to$ let's end points of double ordinate parabola

$y^2=8x$ are $p(2t^2,4y=t)$ & $p^1=(2t^2,-4t)$

$\to$ Double ordinate subtends an angle ${60}^{\circ }$

So, angle is bisected by axis of parabola.

$tan{30}^{\circ }=\frac{4t}{2t^2}$

$tan{30}^{\circ }=\frac{2}{t}$

$\therefore t=\frac{2}{1/\sqrt{3}}$

$t=2\sqrt{3}$

$P(24,8\sqrt{3})$ & $p^1(24,-8\sqrt{3})$

$\to$ length of double ordinate

$p{p}^1=\sqrt{(24-24{)}^2+(8\sqrt{3}-(-8\sqrt{3}){)}^2}$

$=\sqrt{co{s}^2+(16\sqrt{3}{)}^2}$

$p{p}^1=16\sqrt{3}$