Use implicit differentiation to find an equation of the tangent line to the cardioid at the point (0, 0.5).
x^2 + y^2 = (2x^2 + 2y^2 - x)^2
2xdx+2ydy = 2(2x^2+2y^2-x)[4xdx+2ydy-dx]
2(0)dx+2(.5)dy = 2(0+.5-0)(0+1dy-dx)
dy = dy-dx
dx = 0
looks vertical, x = 0