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The perpendicular from the origin to a line meets it at the point $(-2,9)$, find the equation of the line.
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Verified Answer
Let $O N$ be perpendicular to $A B$.
The point is $(-2,9)$
$\therefore \quad$ Slope of $O N=\frac{9-0}{-2-0}=\frac{-9}{2}$
Slope of $A B$ which is perpendicular to $O N=\frac{2}{9}$
( $\because$ Lines are perpendicular if $m_1 m_2=-1$ )
Now, $A B$ passes through $(-2,9)$ and has the slope $\frac{2}{9}$.
$\therefore \quad$ Equation of $A B, y-9=\frac{2}{9}(x+2)$.
or $9 y-81=2 x+4$ or $2 x-9 y+85=0$
The point is $(-2,9)$
$\therefore \quad$ Slope of $O N=\frac{9-0}{-2-0}=\frac{-9}{2}$
Slope of $A B$ which is perpendicular to $O N=\frac{2}{9}$
( $\because$ Lines are perpendicular if $m_1 m_2=-1$ )
Now, $A B$ passes through $(-2,9)$ and has the slope $\frac{2}{9}$.
$\therefore \quad$ Equation of $A B, y-9=\frac{2}{9}(x+2)$.
or $9 y-81=2 x+4$ or $2 x-9 y+85=0$
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