Find an equation for the indicated conic section. Ellipse with foci (3, -2), (-13, -2) and vertices (12, -2), (-22, -2)

Question

Quizplus · Accepted Answer

Since the foci have the same y-coordinate, the major axis is horizontal, and the center of the ellipse is at the midpoint of the foci, which is (-5, -2). The distance from the center to each focus is c=8. The distance between the vertices is 2a=34. The distance between the center and each vertex is a=17. Thus, b is given by the Pythagorean theorem:
b^2 = a^2 - c^2 = 225 - 64 = 161
The equation of the ellipse is then:
(x+5)^2/289 + (y+2)^2/161 = 1
which is equivalent to choice B after simplification.

Find an Equation for the Indicated Conic Section