An ellipse with horizontal and vertical axes is centered at the origin. If the point (4, 2) is on the ellipse, is the point (4, -2) necessarily on the ellipse as well?

Question

Quizplus · Accepted Answer

Since the ellipse is centered at the origin and has horizontal and vertical axes, it is symmetric with respect to both the x-axis and the y-axis. Therefore, if (4, 2) is on the ellipse, its reflection across the x-axis, (4, -2), must also be on the ellipse due to this symmetry.

An Ellipse with Horizontal and Vertical Axes Is Centered at the Origin