Question

9. Write an equation in standard form of an ellipse that is 10 units high and 8 units wide. The center of the ellipse is (0,0)..184 100

Answer 1

You know that the center of this ellipse is at this point:

`(0,0)`

Therefore, it is centered at the Origin.

The Standard form of the equation of a ellipse centered at the Origin, is:

1. When it is horizontal:

`(x^2)/(a^2)+(y^2)/(b^2)=1`

Where:

`a>b`

2. When it is vertical:

`\frac{x^2}{b^2^{}}+\frac{y^2}{a^2^{}}=1`

Where:

`a>b`

It is important to know that the coordinates of the vertices, when it is horizontal, is given by:

`(\pm a,0)`

And the coordinates of the co-vertices are:

`(0,\pm b)`

When it is vertical, the vertices are:

`(0,\pm a)`

And the co-vertices:

`(\pm b,0)`

You know that, in this case, the ellipse is 10 units high and 8 units wide, then you can identify that it is vertical.

Therefore, you can find "a" and "b" as following:

`\begin{gathered} a=(10)/(2)=5 \\ \\ b=(8)/(2)=4 \end{gathered}`

Then, its equation in Standard form is:

`\begin{gathered} \\ \\ \frac{x^2}{16^{}}+\frac{y^2}{25^{}}=1 \end{gathered}`

The answer is: Second option.