Question

Equation of the straight line passing through point of intersection of the line $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$ and is making an angle $\frac{\pi }{4}$ with the line $2x-2y+3=0$ is

• A. $(a+b)x=ab$
• B. $(a+b)x+ab=0$
• C. $(a+b)y=ab$
• D. $aby=a+b$

Answer 1

Answer: (A), (C)

$(a+b)y=ab$

Point of intersection of $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$ is $(\frac{ab}{a+b},\frac{ab}{a+b})$
Given line $2x-2y+3=0$ makes an angle $\frac{\pi }{4}$ with the positive direction of $\text{x-axis}$
$\therefore$ Required line which makes an angle $\frac{\pi }{4}$ with this line will be parallel to $\text{x-axis}$ or $\text{y-axis}$.
$i.ex=\frac{ab}{a+b}\text{or}y=\frac{ab}{a+b}$