Tangent to ellipse at point I am searching for a tangent (or just it's angle) to an ellipse at a specific point on the ellipse (or it's angle to the center of the ellipse).
The equation of the ellipse is $\frac{x^2}{\text{a}^2} + \frac{y^2}{\text{b}^2} = 1$.

a, b, $a$ and the point of the intersection are given and I search for
$b$, the angle of the tangent.

I tried a geometic approach which results a almost accurate angle.
I just take a line at two points, one degree left and right to  and recieve the angle  by using the arc tan of the points.
Is there a more accurate way?

Use implicit differentiation.
$$\frac{x^2}{\text{a}^2} + \frac{y^2}{\text{b}^2} = 1$$
$$\frac{2x}{a^2} + \frac{2yy'}{b^2} = 0$$
$$\frac{2b^2x + 2a^2yy'}{a^2b^2} = 0$$
$$2b^2x + 2a^2yy' = 0$$
$$2a^2yy' = -2b^2x$$
$$y' = \frac{-2b^2x}{2a^2y}$$
$$y' = \frac{-b^2x}{a^2y}$$
That gives you the slope of the tangent line at the point $(x, y)$.
