Question

If the foot of the perpendicular from the origin to a straight line is at the point $(3 - 4)$ . Then, the equation of the line is

• A. $3 x - 4 y = 25$
• B. $3 x - 4 y + 25 =0$
• C. $4 x + 3 y - 25 = 0$
• D. $4 x - 3 y + 25 = 0$

Answer 1

Answer: (A)

Let $P(3, - 4)$ be the foot of the perpendicular from the origin $O$ on the required line.
Then, the slope of $OP=\frac{-4-0}{3-0}=\frac{-4}{3}$
Therefore, the slope of the required line is $\frac{3}{4}$.
Hence, its equation is $y+4=\frac{3}{4}\left(x-3\right)$
$\Rightarrow 4\left(y+4\right)=3\left(x-3\right)$
$\Rightarrow 3x-4y-9-16=0$
$\Rightarrow 3x-4y=25$