First slide

Equation of line in Straight lines

Question

A variable line $\frac{x}{a} + \frac{y}{b} = 1$ is such that a – b = 14. The locus of the midpoint of the line intercepted between the axes is

Easy

A

$x + y = 7$
B

$x - y = 7$
C

$2 x + 3 y = 1$
D

$2 x - 3 y = 1$

Solution

Let P (x , y) be a point on the locus
$i f A (a, 0) B (0, b) t h e n x = \frac{a + 0}{2} y = \frac{0 + b}{2}$
$∴ A = (2 x, 0), B (0, 2 y)$
$∴ a = 2 x, b = 2 y$
$∴ a - b = 14 \Rightarrow x - y = 7$
$∴$ locus x – y = 7

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