For an ellipse with a transverse axis along Y-axis. I am writing some of it's associated equations and a parametric point as follows:
Equation for an ellipse $$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\tag{1}$$
Any point on the ellipse $P(\theta)$
$\left(b\cos \theta,a\sin \theta\right)\tag{2}$
Tangent to an ellipse at $P(\theta)$ $$y=mx\pm\sqrt{b^2m^2+a^2}\tag{3}$$
Where $a \gt b$. I want to use $a$ strictly for a major axis.
I know how to use $(1)$ and $(2)$ together with $y=mx+c$ to get $(3)$.
Is $(2)$ valid?