Solve the equation for an ellipse for y. Assume that y > 0. y^2/a^2 + x^2/b^2 = 1

Multiply each term by a^2b^2:-

b^2y^2 + a^2x^2 = a^2b^2

subtract a^2x^2 from both sides

b^2y^2 = a^2b^2 - a^2x^2

Now divide both sides by b^2

y^2 = a^2 - a^2x^2 / b^2 = a^2 (1 - x^2/b^2)

take positive square root (because y > 0)

y = a sqrt (1 - x^2/b^2)