# How do you write the Ellipse equation in standard form 2(x+4)^2 + 3(y-1)^2 = 24?

Mar 30, 2018

${\left(x + 4\right)}^{2} / {\left(\sqrt{12}\right)}^{2} + {\left(y - 1\right)}^{2} / {\left(\sqrt{8}\right)}^{2} = 1$

#### Explanation:

$2 {\left(x + 4\right)}^{2} + 3 {\left(y - 1\right)}^{2} = 24$ - dividing by $24$, it can be written as

$\frac{2 {\left(x + 4\right)}^{2}}{24} + \frac{3 {\left(y - 1\right)}^{2}}{24} = 1$

or ${\left(x + 4\right)}^{2} / 12 + {\left(y - 1\right)}^{2} / 8 = 1$

or ${\left(x + 4\right)}^{2} / {\left(\sqrt{12}\right)}^{2} + {\left(y - 1\right)}^{2} / {\left(\sqrt{8}\right)}^{2} = 1$

which is the equation of an ellipse with center at $\left(- 4 , 1\right)$,

major axis parallel to $x$-axis is $2 \sqrt{12} = 4 \sqrt{3}$

and minor axis parallel to $y$-axis is $2 \sqrt{8} = 4 \sqrt{2}$

graph{((x+4)^2/12+(y-1)^2/8-1)((x+4)^2+(y-1)^2-0.01)=0 [-11, 3, -2.5, 4.5]}