Find an equation of the ellipse consisting of points P

Question

such that PF1 + PF2 = 12, where F1 = (12, 0) and F2 = (6, 0).?

Answer 1

PF₁ + PF₂ = 12, F₁ = (12, 0) and F₂ = (6, 0).

Let P = (x, y) be the any point on the ellipse.

To find the ellipse equation by using distance formula : .

PF₁ = The distance between P = (x, y) and F₁ = (12, 0).

PF₂ = The distance between P = (x, y) and F₂ = (6, 0).