ellipse equation giving negative number when trying to solve

Question

I am trying to find a point on an ellipse when x is -3 with the equation below.

$$\frac {(x-1)^2}{9}+\frac{y^2}{4}=1$$

when I plug $x$ in and try to solve for y eventually I get a negative number before I square-root both sides and I obviously cant do that. where am I going wrong? is there something I'm missing about the limitations of the equation?

Answer 1

Because this equation describes an ellipse with an semimajor axis of $3$ and a semiminor axis of $2$ centered at $(1, 0)$, you can only solve with $-2\leq x\leq 4$ or $-2\leq y\leq 2$ before going beyond where the ellipse exists.

Answer 2

$$\frac{(x-1)^2}{\frac{2}{9}}+\frac{y^2}{4}=1$$

$$x=-3, y^2=-284$$

It means $x=-3$ is not on the ellipse