Question

The tangents from origin to the parabola $y^2+4=4x$ are inclined at.

• A. 0
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{2}$

Answer 1

The correct option is D

$\frac{\pi }{2}$

Given parabola is,

$y^2=4x-4$

=$4(x-1)$

The tangent at a point $(x_1,y_1)$ is given by

$y{y}_1=4(\frac{x+x_1}{2}-1)$

This passes through (0,0)

$0=4.[\frac{x_1}{2}-1]$

$x_1=2$

$y_1^2=4.\left[1\right]$

$y_1=\pm 2$

$\therefore$ points of contact of tangent are (2,2),(2,-2)

slopes of tangents, $m_1=1,m_2=-1$

$\therefore$ Angle betwwen the tangents=${90}^{\circ }$