Q. The line among the following which touches the parabola $y^{2} = 4ax$, is
A) $x + my + am^{3} = 0$
B) $x - my + {am}^{2} = 0$
C) $x + my - am^{2} = 0$
D) $y + mx + am^{2} = 0$
Explanation
(b)
If the line $y = mx + c$ touches the parbola $y^{2} = 4ax$, then
$y = mx + \frac{a}{m}$
$\Rightarrow \ \ \ my = m^{2}\ x + a\$
$\Rightarrow \ my = x + am^{2}\ \ \left\lbrack replacing\ m\ by\ \frac{1}{m} \right\rbrack$
$\Rightarrow \ x - my + am^{2} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.