# Question #30429

##### 2 Answers

#### Answer:

The standard form is

#### Explanation:

Let's rearrange the equation by completing the squares

This is an ellipse, center

graph{(16x^2+32x+5y^2-10y-59)((x+1)^2+(y-1)^2-0.01)=0 [-11.25, 11.25, -5.625, 5.625]}

#### Answer:

Yes

#### Explanation:

To convert the equation to standard form for ellipses, we need to complete the square.

Note that the standard form for an ellipse is:

or

where

Given the starting equation

Now we can complete the square for x and y:

Now we divide both sides by 80 to make the right-hand side equal to 1 for standard conic form:

Therefore, this conic is a vertical ellipse centered at