Question

The equation of pair of straight lines joining the point of intersection of the curve $x^{2} + y^{2} = 4$ and $y - x = 2$ to the origin, is

• A. $x^{2} + y^{2} = (y - x)^{2}$
• B. $x^{2} + y^{2} + (y - x)^{2} = 0$
• C. $x^{2} + y^{2} = 4(y - x)^{2}$
• D. $x^{2} + y^{2} + 4(y - x)^{2} = 0$

Answer 1

Answer: (A)

$x^{2} + y^{2} = (y - x)^{2}$

Answer 2

Equation can be found by homogenising the curve w.r.t. line.

i.e., $x^{2} + y^{2} = 4\left( \frac{y - x}{2} \right)^{2}$or $x^{2} + y^{2} = (y - x)^{2}$.