# How do you write an equation of an ellipse in standard form given center at origin and passes through (√6, 2) and (-3, √2)?

##### 1 Answer

The standard form is:

#### Explanation:

The standard form of an equation of an ellipse with an arbitrary center

The standard form equation for an ellipse with its center at the origin is:

Write two equations using the above form and the two given points:

Do the multiplication implied by the squares:

Let

Multiply equation [6] by -2 and add to equation [5]

Substitute

The standard form is:

check:

This checks.