Find Cartesian equation from Parametric Equations Including Sec and Tan

Question

Need to find the cartesian equation from:

$$ x = sec^2t - 1 , y = tan t, -\frac\pi2 \lt t \lt \frac \pi2 $$

With sin and cosine I use the unit circle, but I don't know what to do with sec and tangent. Any help would be greatly appreciated.

Answer 1

Hint : $$\tan^2 t + 1 = \sec^2 t$$

Answer 2

HINT:

$$\sec(x) = \frac{1}{\cos(x)}$$ $$\tan(x) = \frac{\sin(x)}{\cos(x)}$$