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To write the equation $Ax^2 + By^2 = C$ in the standard form for ellipses, we divide through by

The $x$ -coordinates of all points on a central ellipse $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ lie between and

In the standard form for an ellipse, $(h, k)$ are the coordinates of the of the ellipse.

The vertical axis of an ellipse $\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$ has length .