Question

The perpendiculars are drawn to lines $L_1$ and $L_2$ from the origin making an angle $\frac{\pi}{4}$ and $\frac{3\pi}{4}$ respectively with the positive direction of X-axis. If both the lines are at unit distance from the origin, then their joint equation is

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

Hint:

Geometry Tip: When multiplying lines to find joint equations, always look for groupings that create a difference of squares. It reduces the chance of algebraic errors compared to distributing every single term manually.

Answer 1

The Correct Option is C