Find the \(\frac{dy}{dx}\) for the curve defined by \((x-y)^2 = y\text{.}\) This is a tilted parabola. Find the equation of the line tangent to the curve at the point \((0,1)\)
Repeat this to explore the cardioid \(x^2 + y^2 - (x^2+y^2-y)^2 = 0\text{.}\) What is the slope of the tangent line at the point \((1,0)\text{?}\) Where is the tangent line horizontal? Where is it vertical?
