Question: Consider the curve given by \({{x}^{2}}+4{{y}^{2}}=7+3xy\)

(a) Show that \(\frac{dy}{dx}=\frac{3y-2x}{8y-3x}\)

(b) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve P is horizontal. Find the y-coordinate of P.

(c) Find the value of \(\frac{{{d}^{2}}y}{d{{x}^{2}}}\) at the point P from part b.