Show by implicit differentiation that the tangent to the ellipse:

x^(2) / a^(2) + y^(2) / b^(2) = 1

at the point (x0, y0) is:

[ (x0x) / a^(2) ] + [ y0y / b^(2) ]

I got my gradient to be y' = -b^(2)x0 / a^(2)y0 but my tangent line was:

y = [ -b^(2)x0 / a^(2)y0 ] + [b^(2)x0^(2) / a^(2)y0^(2)]

Im not sure what the problem may be as I simply subbed in the gradient and (x0,y0) points into the y = mx + c equation