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# State whether the following statement is True or False : The line $lx+my+n=0$ will touch the parabola $y^2=4ax$ if $ln=am^2$

$\begin{array}{1 1}\text{True}\\\text{False}\end{array}$

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• The condition for a line $y=mx+c$ to be a tangent to the parabola is $c=\large\frac{a}{m}$ where $a$ is the focus and $m$ is the slope.
Answer : True
The equation of the given line $=lx+my+n=0$
The equation of the parabola is $y^2=4ax$
The condition for the line to be a tangent to the parabola is $c=\large\frac{a}{m}$
Here $c=-\large\frac{n}{m};$$a=a$ and slope $m=-\large\frac{l}{m}$
$\therefore -\large\frac{n}{m}=\frac{a}{-\Large\frac{l}{m}}$
$\Rightarrow \large\frac{n}{m}=\frac{ma}{l}$
$\Rightarrow ln=am^2$
Hence the statement is True.