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Q.
The perpendicular from the origin to the line $y=m x+c$ meets at the point $(-1,2)$. Then, the value of $m$ and $c$ respectively are
Straight Lines
Solution:
$\because$ Line $O P \perp$ Line $A B$
$ \therefore $ Slope of $ O P \times $ Slope of $ A B =-1 $
$\Rightarrow \frac{2-0}{-1-0} \times m =-1 $
$\Rightarrow -2 m =-1 $
$\Rightarrow m =\frac{1}{2}$
Also, point $(-1,2)$ satisfies the line
$y=m x+c$
i.e., $2=\frac{1}{2}(-1)+c $ (putting $\left.x=-1, y=2\right)$
$\Rightarrow 2=-\frac{1}{2}+c $
$ \Rightarrow c=2+\frac{1}{2}=\frac{5}{2} $
Hence, $ m=\frac{1}{2}, c=\frac{5}{2}$
