A curve called the folium of Descartes is defined by the parametric equations (a) Show that if

Question:

A curve called the folium of Descartes is defined by the parametric equations

(a) Show that if (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y = x. Where does the curve intersect this line?
(b) Find the points on the curve where the tangent lines are horizontal or vertical.
(c) Show that the line y = €“ x €“ 1 is a slant asymptote.
(d) Sketch the curve.
(e) Show that a Cartesian equation of this curve is x3 + y3 = 3xy.