An ellipse with horizontal and vertical axes is centered at the origin. If the point $(3,4)$ is on the ellipse, is the point $(-4,-3)$ necessarily on the ellipse as well?

Name: An ellipse with horizontal and vertical axes is centered at the origin. If the point $(3,4)$ is on the ellipse, is the point $(-4,-3)$ necessarily on the ellipse as well?
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Question

Quizplus · Accepted Answer

An ellipse centered at the origin does not necessarily have symmetry that includes both points $(3,4)$ and $(-4,-3)$ unless it is a circle.

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