First slide

Equation of line in Straight lines

Question

$If \frac{x}{c} + \frac{y}{d} = 1 be any line through the intersection of lines \frac{x}{a} + \frac{y}{b} = 1 and \frac{x}{b} + \frac{y}{a} = 1, then$

Easy

A

$\frac{1}{a} + \frac{1}{d} = \frac{1}{b} + \frac{1}{c}$
B

$\frac{1}{b} + \frac{1}{d} = \frac{1}{c} + \frac{1}{a}$
C

$\frac{1}{c} + \frac{1}{d} = \frac{1}{a} + \frac{1}{b}$
D

$a + b = c + d$

Solution

$Point of intersection of \frac{x}{a} + \frac{y}{b} = 1$ $and \frac{x}{a} + \frac{y}{a} = 1 is (\frac{a b}{a + b}, \frac{a b}{a + b})$
$Putting the point in \frac{x}{c} + \frac{y}{b} = 1, w e g e t \frac{1}{c} + \frac{1}{d} = \frac{1}{a} + \frac{1}{b}$

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