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} *)
