Q. If the parabola $y^{2} = 4ax$ passes through the point$\ (1, - 2)$, then tangent at this point is
A) $x - y - 1 = 0$
B) $x + y + 1 = 0$
C) $x - y + 1 = 0$
D) None of these$\$
Explanation
(b)
Since, point $(1 - 2)$ lies on curve$\ y^{2} = 4ax$
$4 = 4a\ \Rightarrow \ a = 1$
Equation of any tangent to the parabola is
$y = mx + \frac{1}{m}$
It also passes through $(1, - 2).\$
$- 2 = m + \frac{1}{m}$
$\Rightarrow \ m^{2} + 2m + 1 = 0$
$(m + 1)^{2} = 0\ \Rightarrow \ m = - 1$
$\therefore\ y = - x - 1\ \Rightarrow \ x + y + 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.