First slide

Equation of line in Straight lines

Question

A variable line drawn through the point $(1, 3)$ meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed, where $' O'$ is the origin, the locus of $' P'$ is

Very difficult

A

$\frac{1}{y} + \frac{3}{x} = 1$
B

$x + 3 y = 1$
C

$\frac{1}{x} + \frac{3}{y} = 1$
D

$3 x + y = 1$

Solution

Let the line be $\frac{x}{a} + \frac{y}{b} = 1,$ then $\frac{1}{a} + \frac{3}{b} = 1$
$A \equiv (a, 0), B (0, b)$

$\Rightarrow$ $P \equiv (a, b)$

Thus locus of $' p'$ is $\frac{1}{x} + \frac{3}{y} = 1$ .

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