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 (6, 0), and point on graph (0, 8)

Answer 1

Since the center is (0,0) and a focus lies on the x-axis, the equation has the form:

x² / a² + y² / b² = 1, where c² = a² - b²

c = distance from the center to either focus = 6

(0,8) is on the ellipse and is directly above the center. So, (0,8) is an endpoint of the minor axis.

Distance from the center to (0,8) = 8 = (1/2)(length of minor axis) = b/2. So, b = 16.

Since c² = a² - b² and b = 16 and c = 6, a² = 36 + 256 = 292

Equation of ellipse: x² / 292 + y² / 256 = 1