SOLUTION: Please help! Can you include how you came to the answer as well, so I know how to do it myself in the future. Thanks so much! Identify the type of equation presented in x^2+y^2-4

Algebra ->  Equations -> SOLUTION: Please help! Can you include how you came to the answer as well, so I know how to do it myself in the future. Thanks so much! Identify the type of equation presented in x^2+y^2-4      Log On


   

Question 429551: Please help!
Can you include how you came to the answer as well, so I know how to do it myself in the future. Thanks so much!
Identify the type of equation presented in x^2+y^2-4x+12y-6=0
Answer by Gersid(33) About Me  (Show Source):
You can put this solution on YOUR website!
Since the equation includes both an x%5E2 term and a y%5E2 term, it looks like it would be the equation of a conic section.
x%5E2%2By%5E2-4x%2B12y-6+=+0 Start by grouping the x- and y-terms.
%28x%5E2-4x%29%2B%28y%5E2%2B12y%29-6+=+0 Next add 6 to both sides.
%28x%5E2-4x%29%2B%28y%5E2%2B12y%29+=+6 Now complete the square in both x and y.
%28x%5E2-4x%2B4%29%2B%28y%5E2%2B12y%2B36%29+=+6%2B4%2B36 Simplify.
%28x-2%29%5E2%2B%28y%2B6%29%5E2+=+46 Compare this with the general form of the equation of a circle with center at (h, k) and radius r.
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
So what you have is the equation of a circle with its center at (2, -6) and a radius r+=+sqrt%2846%29.