# How do you identity if the equation #x^2+y^2+6y+13=40# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

It is a circle.

You graph it by:

- set your compass to a radius of
#sqrt365/2# - put the center at the point
#(-13/2, -3)# - draw the circle.

#### Explanation:

I suspect that the intended equation is:

Otherwise, the 13 and 40 would have been combined into a single constant term.

The reference [Conic Section](https://en.wikipedia.org/wiki/Conic_section

graph{x^2+y^2+6y+13x=40 [-30, 30, -15, 15]}

We can make fit the general Cartesian form for the equation of a circle:

where

By completing the squares:

We know, from their respective binomial expansions, that:

Solve for h and k:

We can obtain a value for r by substituting these values to the right side of equation [1.1}:

Substituting these values into equation [2]:

This is the standard Cartesian form with its center at