Question

Let y = f(x) be the continuous function that satisfies the equation x^4 - (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2.
(a) Find and expression for y'.
(b) Write an equation for the line L.
(c) Give the coordinates of a point that is on the graph of f but is not on line L.
(d) Give the coordinates of a point that is on the line L but is not on the graph of f.

Answer 1

I will be happy to critique your thinking or work.

Answer 2

I think a0 is (-4x^3+10xy^2)/(-10x^2y+16y^3)
and that makes b y=1/2x. However, I can't seem to get anything for c nor d. How do I start?

Answer 3

Hmm. Don't know...