Question

The condition that the straight line $lx+my+n=0$ touches the parabola $x^2=4ay$ is

• A. $bn=a{m}^2$
• B. $a{l}^2-mn=0$
• C. $ln=a{m}^2$
• D. $am=l{n}^2$

Answer 1

The correct option is B $a{l}^2-mn=0$

we can write $lx+my+n=0$ in from of $y=Mx+c$
So, $my=-lx-n$
$y=-\frac{lx}{m}-\frac{n}{m}$
comparing with $y=Mx+c$
$M=-\frac{l}{m},c=-\frac{n}{m}$
For line to touch parabola $x^2=4ay,$
$c=-a{M}^2$
$\Rightarrow a{l}^2=mn$