First slide

Equation of line in Straight lines

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

Moderate

A

$x + y = a b$
B

$x + y = a + b$
C

$a x + b y = a^{2}$
D

$b x + a y = b^{2}$

Solution

The line $\frac{x}{a} - \frac{y}{b} = 1$ cuts $x -$ axis at $P (a, 0) .$ The equation of the line through $P (a, 0)$ and perpendicular to $\frac{x}{a} - \frac{y}{b} = 1,$ is
$y - 0 = - \frac{a}{b} (x - a) \Rightarrow a x + b y = a^{2}$

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