Q. From the point $( - 1, - 6)$ two tangents are drawn to the parabola $y^{2} = 4x$. Then, the angle between the two tangents is
A) $30{^\circ}$
B) $45{^\circ}$
C) $60{^\circ}$
D) $90{^\circ}$
Explanation
(d)
Equation of tangent to $y^{2} = 4x\$is $y = mx + \frac{1}{m}$
Since, tangent passes through $( - 1,\ - 6)$
$\therefore - 6 = - m + \frac{1}{m}\ \Rightarrow \ m^{2} - 6m - 1 = 0$
Here, $m_{1}m_{2} = - 1$
$\therefore$ Angle between them is$\ 90{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.