Question

The sum of the x-coordinates of the intersection of $x^2+y^2=36$ and $x^2-y^2=6$, is______.

• A. $-2\sqrt{21}$
• B. $0$
• C. $2\sqrt{15}$
• D. $2\sqrt{21}$

Answer 1

Answer: (B)

$0$

$x^2+y^2=36\dots eqn\left(2\right)$ (circle of radius 6)

$x^2-y^2=6\dots eqn\left(2\right)$ (hyperbola with the vertex $(\sqrt{6},0)$)

they intersect each other at 4 points and each two of them have the same x coordinate.

Adding both equations, to find the x coordinate of the intersecting point, we get

$2x^2=42x=\pm \sqrt{2}1,\pm \sqrt{2}1$

The sum of the x-coordinates of the intersection $=0$