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

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 $y+4=\frac{3}{4}\left(x-3\right)$
$\Rightarrow 4\left(y+4\right)=3\left(x-3\right)$
$\Rightarrow 3x-4y-9-16=0$
$\Rightarrow 3x-4y=25$