Question

Find the constant sum for an ellipse with foci F1 (2, 0), F2 (-6, 0) and the point on the ellipse (2, 6).

Answer 1

PF1 + PF2 = 2a

Answer 2

\[\sqrt{(x_1-2)^2+(y_1-6)^2}+\sqrt{(x_2-2)^2+(y_2-6)^2}\]

Answer 3

sorry it took so long my internet is bugging out

Answer 4

so 16

Answer 5

If constant term refers to the sum of the distance from the two foci (which is actually constant for any point on the ellipse, actually the basic definition of it), then the constant term is equal to the length of the major axis.

Answer 6

the length of the major axis is also equal to the sum of the distance of any point on the ellipse from the two foci. Why?
remember the basic definition? no?
check this video out, should help:
http://www.youtube.com/watch?v=4xF5CqTrG2Y
(focus on the r+r' value being constant there as the point moves)

after this, you should realise that you just add the distance of the point from each foci. that is the major axis, and the-constant-term!

Answer 7

Draw a picture! The distance from the point (2,6) to the focus (2,0) is 6. The distance from the point (2,6) to the second focus (-6,0) is easy to calculate because this is the hypotenuse of a (3:4:5) right triangle.