Well your method is right but i would suggest you another method that you can use the formula of :
tanθ = ± m1 + m2
1 + m1m2
You will get answer in the form of m. Then you can find the value by elimination method.
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.
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?
Here's my working.
The equation of the tangent at is easily shown to be:and the gradient at isHere and at A. So the gradient at A is:and the tangent at A is
(* Incidentally, the gradient of a diameter isn't . It's .)