Unparametrize $x = 7 cos t, y = 4 tan t$

Question

"Express the given parametrization in the form $y = f(x)$ by eliminating the parameter.

$x = 7 \cos t, y = 4\tan t$"

$y=\pm4 \sqrt {\frac {49} {x^2} - 1}$

Is correct?

Answer 1

HINT: Notice, we have $x=7\cos t\implies \color{red}{\cos t=\frac{x}{7}}$ & $y=4\tan t \implies \color{red}{\tan t=\frac{y}{4}}$

We know that $$\tan t=\frac{\sin t}{\cos t}=\pm \frac{\sqrt{1-\cos ^2 t}}{\cos t}=\pm\sqrt{\frac{1}{\cos^2 t}-\frac{\cos^2 t}{\cos^2 t}}$$ $$\tan t=\pm\sqrt{\left(\frac{1}{\cos t}\right)^2-1}$$

Now, set the corresponding value of $\tan t$ & $\cos t$ to find the answer