Question

If the lines joining the origin to the points of intersection of a line $L$ and $x^2 + y^2 = 4$ are the coordinate axes, then the equation of the line $L$ is

• A. $x + y = 2$
• B. $x + y = 4$
• C. $x + y = 1$
• D. $x + y = 0$

Hint:

Homogenization Insight: If two points lie on a circle and their joining lines with origin are coordinate axes, the intersecting line must pass through intercepts $(\pm r, 0)$ and $(0, \pm r)$ of the circle.

Answer 1

The Correct Option is A

Let $L$ intersect the circle $x^2 + y^2 = 4$ at points lying on $x$-axis and $y$-axis. Points: $(2,0)$ and $(0,2)$ satisfy the circle and lie on the axes.
Equation of line through them: $\frac{x}{2} + \frac{y}{2} = 1 \Rightarrow x + y = 2$