Question

ONLY NEED PART (B) HELP: Consider the ellipse with the equation x^2+2y^2-6x+8y=21. part a asks to use implicit differentiation which i did to find the slope of the tangent line. I got y'=(3-x)/4+2y). Part b is where I am confused: Do we need the technique of implicit differention here: Note that the curve's formula is a quadratic in y; what happens when we try solving for y to use ordinary techniques of differentiation?

Answer 1

the "ordinary technique" would be to solve for y in
x^2+2y^2-6x+8y=21
and then take the derivative
because it is a quadratic, you will get two solutions for y
(besides being very messy)

Answer 2

Thank you!