First slide

Parabola

Question

A line bisecting the ordinate $P N$ of a point $P (a t^{2}, 2 a t), t > 0,$ on the parabola $y^{2} = 4 a x$ is drawn parallel to the axis to meet the curve at $Q$ . If $N Q$ meets the tangent at the vertex at the point T, then the coordinates of T are.

Moderate

A

$(0, 4 a t / 3)$
B

$(0, 2 a t)$
C

$(a t^{2} / 4, a t)$
D

$(0, a t)$

Solution

Equation of the line parallel to the axis and bisecting the ordinate PN of the point $P (a t^{2}, 2 a t)$ is $y = a t$ which meets the parabola $y^{2} = 4 a x$ at the point $Q (\frac{a t^{2}}{4}, a t)$ Coordinates of $N$ are $(a t^{2}, 0)$ . Equation of $N Q$ is
$y = \frac{0 - a t}{a t^{2} a t^{2} / 4} (x - a t^{2})$
which meets the tangent at the vertex, $x = 0,$ at the point $y = 4 a t / 3$ .

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