How do I find the center of an ellipse in standard form?

Oct 19, 2014

An ellipse in standard form looks like

${\left(x - h\right)}^{2} / {a}^{2} + {\left(y - k\right)}^{2} / {b}^{2} = 1$

or

${\left(x - h\right)}^{2} / {b}^{2} + {\left(y - k\right)}^{2} / {a}^{2} = 1$

where $a \ge b$.
However, for your question, we don't need to be concerned with $a$ and $b$

An ellipse in standard form is centered at (h, k).

For example,

${\left(x - 1\right)}^{2} / 1 + {\left(y + 2\right)}^{2} / 4 = 1$ is centered at (1, -2)

${x}^{2} / 16 + {\left(y - 5\right)}^{2} / 9 = 1$ is centered at (0, 5)