# 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?

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.

I suspect that the intended equation is:

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

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:

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]:

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To identify the type of conic section represented by the equation (x^2 + y^2 + 6y + 13 = 40), we need to rearrange it into a standard form. Completing the square for the (y)-terms yields:

[x^2 + y^2 + 6y + 13 = 40 ] [x^2 + (y^2 + 6y + 9) + 13 - 9 = 40 ] [x^2 + (y + 3)^2 = 36 ]

Now, the equation is in the form (x^2 + (y - k)^2 = r^2), which represents a circle with center ((0, -3)) and radius (6). Therefore, the given equation represents a circle.

To graph it:

- Plot the center of the circle, which is at ((0, -3)).
- Use the radius of (6) to plot points on the circle. You can plot points ((0, 3)), ((6, 0)), ((0, -9)), and ((-6, 0)) to help draw the circle.
- Sketch the circle through these points, ensuring it is symmetrical around the center ((0, -3)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do I find the vertex of #y=(x+2)^2-3#?
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