Finding intersection between a quadratic equation and linear equation

Question

Is it possible that you find a quadratic equation that NEVER intersects the linear equation y=x?

I believe that it is impossible. I tried as many equations as I could such as y=(x+10)^2 and x=(y+10)^2, yet there seems to be none that do not intersect the equation.

Answer 1

y=x and y=(x+5)^2 do not intersect