Question

Find the equation of the tangent line to the curve at the point (-4,-2). THe equation is x^2 + xy + 2y^2 = 32

Answer 1

tangent line
\[y+2 = \frac{dy}{dx}(x+4)\]
just find dy/dx using implicit differentiation
\[\rightarrow 2x + (y+x \frac{dy}{dx}) +4y \frac{dy}{dx} = 0\]