Question

The joint equation of pair of straight lines passing through origin and having slopes $(1+\sqrt{2})$ and $\left(\frac{1}{1+\sqrt{2}}\right)$ is ________.

• A. $x^2-2\sqrt{2}xy+y^2=0$
• B. $x^2-2\sqrt{2}xy-y^2=0$
• C. $x^2+2xy-y^2=0$
• D. $x^2+2xy+y^2=0$

Answer 1

The correct option is A $x^2-2\sqrt{2}xy+y^2=0$

Equation of straight line passing through origin is $y=mx$

So, Equation of first straight line is $y=(1+\sqrt{2})x$

Equation of second straight line is $y=\left(\frac{1}{1+\sqrt{2}}\right)x$

Now their combined equation is $\{y-(1+\sqrt{2}\left)x\right\}\{y-(\frac{1}{1+\sqrt{2}}\left)x\right\}=0$ which simplifies to $x^2-2\sqrt{2}xy+y^2=0$