AB is a diameter of the ellipse

the eccentric angle at A is

. Find

a) the eccentric angle of B

b) the equations of the tangent at A and B

c) the equation of the conjugate diameter

I found correctly the eccentric angle of B to be

When I did (b) and (c), I used

to find the gradient of the tangent and conjugate diameter.

Grandad says: No. See below*
But I found that in the answers the gradients are all

which is the gradient of the diameter AB.

I used the equation for tangents

Have I misunderstood something?

Thanks