Question

The condition sot that the line $lx+my+n=0$ may touch the parabola $y^2=8x$, is

• A. $8m^2=lm$
• B. $2m^2=ln$
• C. $m^2=8ln$
• D. $m^2=2ln$

Answer 1

The correct option is B $2m^2=ln$

Given equation of the line is $lx+my+n=0$
$\Rightarrow my=-lx-n$
$\Rightarrow y=\frac{-l}{m}x-\frac{n}{m}$
On comparing with $y=Mx+C$, we get
$M=\frac{-l}{m}$ and $C=\frac{-n}{m}$ ....(i)
Again, given equation of the parabola is $y^2=8x$
On comparing with $y^2=4ax$, we get
$4a=8$ $\Rightarrow$ $a=2$
Now, by condition of tangency,
$C=\frac{a}{M}$
$\Rightarrow \frac{-n}{m}=\frac{2}{-l/m}$ [from equation (i)]
$\Rightarrow \frac{n}{m}=\frac{2m}{l}\Rightarrow ln=2m^2$.