Question

Find the equation that is satisfied by the set of points such that the sum of the distances from the point to (2,0) and (-2,0) is 6. Express your answer in standard form.

Answer 1

Since you want the equation in standard form, you must be familiar with the values of a, b, and c as they relate to the ellipse.

here c = 2 and 2a = 6 or a = 3
in a standard ellipse
b^2 + c^2 = a^2
b^2 + 4 = 9
b^2 = 5

so

x^2/9 + y^2/5 = 1 is your equation.