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Question

Let F_1 = (0,1) and F_ 2= (4,1). Then the set of points P such that PF_1 + PF_2 = 6form an ellipse. The equation of this ellipse can be written as (x - h)^2a^2 + (y - k)^2b^2 = 1.Find h + k + a + b.

Accepted Answer

We have that 2a = 6, so a = 3. The distance between the foci is 2c = 4, so c = 2. Hence, b = a^2 - c^2 = 5. The center of the ellipse is the midpoint of F_1 F_2, which is (2,1). Thus, the equation of the ellipse is (x - 2)^23^2 + (y - 1)^2(5)^2 = 1.Hence, h + k + a + b = 2 + 1 + 3 + 5 = 6 + 5.