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?

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?