Short Answer

Determining Vertices for an Elliptical Component

A machinist is fabricating an elliptical component according to the design equation (x+3)24+(y5)216=1\frac{(x+3)^2}{4} + \frac{(y-5)^2}{16} = 1. The component's center is located at (3,5)(-3, 5). To correctly cut the vertical dimension of the piece, the machinist needs to know the distance from the center to the top and bottom vertices, as well as the specific coordinates of those vertices. Based on the equation, what is the distance from the center to each vertex along the vertical axis, and what are the coordinates of these two vertices?

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Updated 2026-05-25

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