Q. If the straight line $lx + my + n = 0$ touches the parabola, $y^{2} = 4ax$, then
A) $nm = al^{2}$
B) $nl = am^{2}$
C) $nl = am$
D) $ml = an^{2}$
Explanation
(b)
Given equation of line is $lx + my + n = 0\ or\ y = - \frac{lx}{m} - \frac{n}{m}$ and equation of parabola $y^{2} = 4ax$
Condition for tangency
$\left( - \frac{n}{m} \right) = \frac{a}{- l/m}$
$\Rightarrow \ nl = am^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.