# How do you write an equation of an ellipse in standard form with centre at (-2,8) and a major axis (parallel to the x-axis) length of 12 units and a minor axis of 10 units?

Sep 13, 2016

We know that the standard equation of an ellipse having coordinate of its center $\left(\alpha , \beta\right)$ , major axis parallel to x-axis and length of the semi-major axis and semi-minor axis as $a \mathmr{and} b$ respectively ,is

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

Inserting

$\alpha = - 2 \mathmr{and} \beta = 8$

$a = \frac{12}{2} = 6 \mathmr{and} b = \frac{10}{2} = 5$

we get the standard equation of the ellipse

${\left(x + 2\right)}^{2} / {6}^{2} + {\left(y - 8\right)}^{2} / {5}^{2} = 1$