I have just learned about parametric equations. I have gotten the concept of turning the parametric equations to regular/ordinary equations, but am having trouble doing the reverse in this problem:
The graph of the equation $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$ is an ellipse with center $(h,k)$, horizontal axis length $2a$, and vertical axis length $2b$. Find parametric equations whose graph is an ellipse with center $(h,k)$, horizontal axis length $2a$, and vertical axis length $2b$, and explain why your answer is correct.
I have tried making an equation with just $x=\sin t+b$ and $y=\cos t+d$, but have not gotten anywhere past this.
hint: $$\dfrac{x-h}{a} = \cos \theta, \dfrac{y-k}{b} = \sin \theta, \theta \in [0,2\pi)$$