Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Een ellips, betrokken op haar symmetrieassen, heeft 5 als halve grote as en 3 als halve kleine as. Haar parametervoorstelling luidt
$https://latex.codecogs.com/png.image?\dpi{110}\left\{\begin{matrix}x=3\cos\alpha \\y=5\sin\alpha\end{matrix}\right.\; \left\{\begin{matrix}x=3\sin \alpha\\y=5\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\lambda ^2 \\y=3\lambda \end{matrix}\right.\;\left\{\begin{matrix}x=5\tan \alpha\\y=3\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\cos\alpha \\y=3\sin\alpha\end{matrix}\right.$
A	B	C	D	E

Given is an ellipse (2a=length of Major Axis ; 2b=length of Minor Axis) Her equations in parametric form are
$https://latex.codecogs.com/png.image?\dpi{110}\left\{\begin{matrix}x=3\cos\alpha \\y=5\sin\alpha\end{matrix}\right.\; \left\{\begin{matrix}x=3\sin \alpha\\y=5\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\lambda ^2 \\y=3\lambda \end{matrix}\right.\;\left\{\begin{matrix}x=5\tan \alpha\\y=3\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\cos\alpha \\y=3\sin\alpha\end{matrix}\right.$ -------- A -------------- B ----------- C ----------D --------------- E ----

Given is an ellipse
(2a=length of Major Axis ;
2b=length of Minor Axis)
Her equations in parametric form are

$https://latex.codecogs.com/png.image?\dpi{110}\left\{\begin{matrix}x=3\cos\alpha \\y=5\sin\alpha\end{matrix}\right.\; \left\{\begin{matrix}x=3\sin \alpha\\y=5\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\lambda ^2 \\y=3\lambda \end{matrix}\right.\;\left\{\begin{matrix}x=5\tan \alpha\\y=3\cos\alpha\end{matrix}\right.\;\left\{\begin{matrix}x=5\cos\alpha \\y=3\sin\alpha\end{matrix}\right.$
-------- A -------------- B ----------- C ----------D --------------- E ----

$\\ \text{x en y moeten voldoen aan de vergelijking van de ellips: } \frac{x^2}{5^2}+\frac{y^2}{3^3}=1\\ \text{Voor E. lukt dat. Immers: } \frac{(5.\cos\alpha)^2}{5^2}+\frac{(3.\sin\alpha)^2 }{3^3}=1 ,\\ \text{ rekening houdend met de grondformule}$