The equation of the line passing through the origin and the point of intersection of the lines x a + y b = 1 and x b + y a = 1 is

Question

The equation of the line passing through the origin and the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ is

Smart Achievers · Accepted Answer

(4)

$Given equation of lines are$

$\frac{x}{a} + \frac{y}{b} = 1,$ $\frac{x}{b} + \frac{y}{a} = 1$

$or$ $b x + a y = a b$ ...(i)

$a x + b y = a b$ ...(ii)

$Solving (i) and (ii),$

$x = \frac{a b}{a + b},$ $y = \frac{a b}{a + b}$

$So equation of line passing through (0,0) is$

$y - 0 = \frac{\frac{a b}{a + b}}{\frac{a b}{a + b}} (x - 0) \Rightarrow y = x$

Solution

Q.
The equation of the line passing through the origin and the point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ is

1 $b x - a y = 0$

2 $x + y = 0$

3 $a x - b y = 0$

4 $x - y = 0$

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Solution

Q. The equation of the line passing through the origin and the point of intersection of the lines xa+yb=1 and xb+ya=1 is

1 bx-ay=0

2 x+y=0

3 ax-by=0

4 x-y=0