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 , so let’s plug that into the circle equation and solve for .

This makes sense. is a line that goes through the origin, and is a circle centered on the origin. So we know we’ll either have a negative and a negative , or we’ll have a positive and a positive .

So let’s just plug the positive -value back into .

Now all that’s left is multiplication. The question asks for the value of .