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.


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.

So let’s just plug the positive x-value back into y=2x.


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


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