Find the equations of the tangent and normal to the curve $2y{{x}^{3}}-xy+5{{y}^{2}}+9=0$ at the poi

Question

Find the equations of the tangent and normal to the curve $2y{{x}^{3}}-xy+5{{y}^{2}}+9=0$ at the point $\left( -2,1 \right)$.

Accepted Answer

$Tangent: 4y = 23x + 50; Normal: 23y = -4x + 15$

Worked Example 1