Ellipses have multiple definitions, how are these the same?

A link to the full video is at the bottom of the screen. Or, for reference: The full video this comes from proves why slicing a cone gives the same shape as the two-thumbtacks-and-string construction, which is beautiful. Editing from long-form to short by Dawid Kołodziej ... #3Blue1Brown #Mathematics #three_blue_one_brown #3_blue_1_brown #3b1b #3brown1blue #3_brown_1_blue #three_brown_one_blue 20240119 -3jPW_TGATI