Parametrisation conic

Question

Consider the conic with the equation

$5x^2+16y^2=45$

write down the parametrisation for the part of the conic that lies in the second quadrant.

how?!

Answer 1

Take $x = t, y = \dfrac{\sqrt{45 - 5t^2}}{4}, -3 \le t \le 0$.

Answer 2

Hint: turn it in form of below $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\$$then compare with $\sin^2t+\cos^2t=1$ so $$\frac{x}{a}=\cos t\\\frac{y}{b}=\sin t.$$