Question

Distance of the point $(2,5)$ from the line $3x+y+4=0$ measured parallel to the line $3x-4y+8=0$ is

• A. $\frac{15}{2}$
• B. $\frac{9}{2}$
• C. $5$
• D. none of these

Answer 1

The correct option is C $5$

Let distance be 'r'.
Co-ordinates of 'P' are
$(2+rcos\theta ,5+rsin\theta )$ where $tan\theta =\frac{3}{4}$
which lies on the line $3x+y+4=0$
$3(2+rcos\theta )+5+rsin\theta +4=0$
$r(3.\frac{4}{5}+\frac{3}{5})+15=0\Rightarrow r=-\frac{15}{3}=-5$
But distance can not be negative
$\therefore r=5$