The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. The locus of mid point of AB is

The straight line passing through the point (8,4) and cuts y-axis at B and x-axis at A. The locus of mid point of AB is

A
$xy + 2 x + 4 y = 64$
B
$xy - 2 x - 4 y = 0$
C
$xy - 4 x - 2 y + 8 = 0$
D
$xy + 4 x + 2 y = 72$

Solution:

Let the eq of $AB i s \frac{x}{a} + \frac{y}{b} = 1$ ……(1)

Let p(h,k) locus of mid point of AB.

$\Rightarrow \frac{x}{2 h} + \frac{y}{2 k} = 1$ through the point $(x, y) = (8, 4)$

$\Rightarrow \frac{1}{2} (8 k + 4 h) = hk$

$∴$ The locus of p is $xy - 2 x - 4 y = 0$

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