Use the given information about the graph of an ellipse to determine its equation. center at the origin, symmetric with respect to the x- and y-axes, focus at (8, 0), and point on graph (0, 6)

Answer 1

x^2/100+ y^2/36 = 1 is an ellipse with center at the origin, focus at (8,0) and includes (0,6)

(x/10)^2 + (y/6)^2 = 1 or

36x^2 + 100y^2 = 3600

the other focus is (-8,0) because the ellipse is symmetric about x=0

the top of the ellipse is (0,6), bottom most point is (0,-6)

left end is (-10,0) right end is (10,0)

an ellipse is defined as the collection of all points such that the sum of their distances to the foci (or focuses) is equal.

(0,6) to each focus is 10. 10+10=20

right end of the ellipse is x-8 + 16+ x-8 = 20

2x = 20

x = 10

right end is (10,0)

10-8 + 16 +10-8 = 20

distance from (-8,0) to (10,0) is 18

distance from (8,0) to (10,0) is 2

18+2 = 20

x^2/a^2 + y^2/b^2 = 1 is the general equation for an ellipse with center at the origin and semi-axis of a on the horizontal axis, a=10, b=6 = the semi axis of the ellipse on the vertical axis