# ellipse

#### veronica1999

##### Member
How do I graph this ellipse?

It doesn't seem to be in the right form.

(x+2)^2 /5 + 2 (y-1)^2 = 1

I don't know what to do with the 2 in front of the (y-1)^2

Doesn't an ellipse have to be x^2/a^2 + y^2/b^2 = 1

#### Sudharaka

##### Well-known member
MHB Math Helper
How do I graph this ellipse?

It doesn't seem to be in the right form.

(x+2)^2 /5 + 2 (y-1)^2 = 1

I don't know what to do with the 2 in front of the (y-1)^2

Doesn't an ellipse have to be x^2/a^2 + y^2/b^2 = 1
Hi veronica1999,

Yes, an ellipse has its equation as, $$\displaystyle\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ if its major and minor axes coincides with the $$x$$ and $$y$$ axes of the Cartesian coordinate system. In this case the center point of the ellipse is at the origin. However a ellipse with its center point at, $$(x_{0},y_{0})$$ has an equation of the form,

$\frac{(x-x_{0})^2}{a^2} + \frac{(y-y_{0})^2}{b^2} = 1$

In your case the ellipse is centered at, $$(-2,1)$$. Now you should be able to draw your ellipse.

Kind Regards,
Sudharaka.

#### veronica1999

##### Member
Thanks.
But I am still not sure what to do with the 2 in front of the (y-1)^2.
Could it have been a mistype meaning (y-1)^2/2 instead of 2(y-1)^2?

#### Sudharaka

##### Well-known member
MHB Math Helper
Thanks.
But I am still not sure what to do with the 2 in front of the (y-1)^2.
Could it have been a mistype meaning (y-1)^2/2 instead of 2(y-1)^2?
Of course not. You can rearrange the equation by taking that $$2$$ to the denominator like this,

$\frac{(x+2)^2}{5} + \frac{(y-1)^2}{\frac{1}{2}} = 1$

Is it clear to you now?

Yes!!!!

Thank you!!!

#### Sudharaka

##### Well-known member
MHB Math Helper
Yes!!!!

Thank you!!!
You are welcome. I am glad to be of any help.