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Q.
The distance of the point $(2,3)$ from the line $2 x-3 y+9=0$ measured along a line $x-y+1=0$ is :
Straight Lines
Solution:
Let coordinates of point $P$ by parametric form
$P\left(2+r \cos 45^{\circ}, 3+r \sin 45^{\circ}\right)$
It satisfies the line $2 x-3 y+9=0$
$\therefore 2\left(2+\frac{r}{\sqrt{2}}\right)-3\left(3+\frac{r}{\sqrt{2}}\right)+9=0 $
$\Rightarrow r=4 \sqrt{2}$
