Question

Find the value of k if the perpendicular distance of P (1, 2) from (4x - 3y + k) = 0 is 5 units.

• A. 15
• B. -35
• C. -15
• D. 35

Answer 1

Answer: (A), (B)

The correct options are
A

15

B

-35

Perpendicular distance of $P(x_1,y_1)$ from ax+by+c=0 is given by $|\frac{a{x}_1+b{y}_1+c}{\sqrt{a^2+b^2}}|$.
$\Rightarrow 5=|\frac{4+6+k}{\sqrt{3^2+4^2}}|$
$5=|\frac{k+10}{5}|$
$\Rightarrow \frac{k+10}{5}=+5or\frac{k+10}{5}=-5$
$\Rightarrow k=15ork=-35$