Q. $ax + by - a^{2} = 0,\$where $a,b$ are non-zero, is the equation to the straight line perpendicular to a line $l$ and passing through the point where $l$ crosses the $x$-axis. Then, equation to the line $l$ is
A) $\frac{x}{b} - \frac{y}{a} = 1$
B) $\frac{x}{a} - \frac{y}{b} = 1$
C) $\frac{x}{b} + \frac{y}{a} = ab$
D) $\frac{x}{a} - \frac{y}{b} = ab$
Explanation
(b)
Equation of line perpendicular to $ax + by - a^{2} = 0$ is $bx - ay + \lambda = 0$ and line
$ax + by - a^{2} = 0\ is\ passes\ through\ \left( –\frac{\lambda}{b}\ ,0 \right),\ then$
$\lambda = - ab$
$\therefore\ bx - ay = ab$
$\Rightarrow \ \frac{x}{a} - \frac{y}{b} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.