in the xy plane, point (x,y) lies on the circle with equation x^2+y^2=1 and on the line with the equation y=2x what is the value of xy?

in the xy plane, point (x,y) lies on the circle with equation x^2+y^2=1 and on the line with the equation y=2x what is the value of xy?
It sat math subject test level 1
Thanks in advance 🙂

Let’s get this by substitution. We know $y=2x$ , so let’s plug that into the circle equation and solve for $x$ .

$x^2+(2x)^2=1\\x^2+4x^2=1\\5x^2=1\\x^2=\dfrac{1}{5}\\\\x=\pm\dfrac{1}{\sqrt{5}}\\\\x=\pm\dfrac{\sqrt{5}}{5}$

This makes sense. $y=2x$ is a line that goes through the origin, and $x^2+y^2+1$ is a circle centered on the origin. So we know we’ll either have a negative $x$ and a negative $y$ , or we’ll have a positive $x$ and a positive $y$ .