Question

The line $\frac{x}{a}-\frac{y}{b}=1$ cuts the $x-$ axis at $P$ . The equation of the line through $P$ perpendicular to the given line is:

• A. $x+y=ab$
• B. $x+y=a+b$
• C. $ax+by=a^{2}$
• D. $bx+ay=b^{2}$

Answer 1

Answer: (C)

Given equation of a line is
Its slope is $\frac{b}{a}$.
$\therefore$ The equation of line passing through a point
$P(a, 0)$ and perpendicular to the given line whose slope is
$-\frac{a}{b}$, is $y-0=-\frac{a}{b}(x-a)$
$b y+a x=a^{2}$