SOLUTION: 18. Classify the conic section of the equation x^2 + 2x + y^2 + 6y = 15. A circle B ellipse C hyperbola D parabola E point F line I'm not sure how I go about classify

Question 162030: 18. Classify the conic section of the equation x^2 + 2x + y^2 + 6y = 15.
A circle
B ellipse
C hyperbola
D parabola
E point
F line

I'm not sure how I go about classifying this. I appericiate any help you have to offer. Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Take half of the "x" coefficient to get . Now square 1 to get 1. Add this value to both sides (on the left, add it right after the "x" term)

Take half of the "y" coefficient to get . Now square 3 to get 9. Add this value to both sides (on the left, add it right after the "y" term)

Combine like terms.

Group the terms into two groups (with three terms in each group)

Factor to get

Factor to get

Rewrite as . Rewrite as

Replace 25 with

Notice how the equation now fits the form where in this case , and . So this shows us that is a circle. So the answer is A
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