How do I find the equation of an Ellipse with the Foci (4,0) (-4,0)?

Questions
1

How do I find the equation of an Ellipse with the Foci (4,0) (-4,0)? It passes through the point (-4,1.8). I’m not sure how to solve this without any additional information.

2

Equation of an ellipse centered on (0, 0) with major axis on the x-axis

ClearAll[x, y, a, b];

eq1 = x^2/a^2 + y^2/b^2 == 1
eq2 = c^2 == a^2 - b^2

Substitute known values

eq1s = eq1 /. {x -> -4, y -> Rationalize@1.8}
eq2s = eq2 /. c -> 4

Solve

sol = Solve[eq1s && eq2s && b > 0 && a > b, {a, b}, Reals]
(* {{a -> 5, b -> 3}} *)

Substitute

eq1 /. sol
(* {x^2/25 + y^2/9 == 1} *)