Q. Consider the following statements : 1. The equation of the parabola whose focus is at the origin is $y^{2} = 4a(x + a)$ 2. The line $lx + my + n = 0$ will touch the parabola $y^{2} = 4ax$, if $\ln = am^{2}$ Which of these is/are correct
A) Only (1)
B) Only (2)
C) Both of these
D) None of these
Explanation
(c)
(1) Given equation of parabola is
$y^{2} = 4a(x + a)$ or $Y^{2} = 4aX$
$\therefore$ focus is $(a,\ 0)$
$\Rightarrow x + a = a,\ y = 0$
$\Rightarrow x = 0,\ y = 0$
$\therefore$ Focus is at origin $(0,\ 0)$
(2) Given equation of line is $y = - \frac{lx}{m} - \frac{n}{m}$
It will touch the parabola $y^{2} = 4ax$, if
$- \frac{n}{m} = \frac{a}{- \frac{l}{m}} \Rightarrow nl = am^{2}$
$\therefore$ Both statements are true
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.