Question

What is the equation of the ellipse with foci (5, 0), (-5, 0) and co-vertices (0, 4), (0, -4)?

Answer 1

The curve equation y3 + 3yx - x3 = 9

Differentiate implicitly with respect to x.

3y2(dy/dx) + 3[y + x(dy/dx)] - 3x2 = 0

3y2(dy/dx) + 3y + 3x(dy/dx)] = 3x2

(dy/dx)(3y2 + 3x) = 3x2 - 3y

dy/dx = 3(x2- y)/3(y2 + x)

dy/dx = (x2- y)/(y2 + x)