SOLUTION: What type of graph is: 5x^2+2y^2+30x-16y+67=0

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Question 739366: What type of graph is:
5x^2+2y^2+30x-16y+67=0
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
ellipse
it can also be written
5(x+3)^2+2(y-4)^2-10 = 0

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
it is an ellipse


5x%5E2%2B2y%5E2%2B30x-16y%2B67=0........group like terms
%285x%5E2%2B30x%29%2B%282y%5E2-16y%29%2B67=0....complete square
%285x%5E2%2B30x%2B___%29%2B%282y%5E2-16y%2B___%29%2B67=0
%285x%5E2%2B30x%2B45%29-45%2B%282y%5E2-16y%2B32%29-32%2B67=0
%285x%5E2%2B30x%2B45%29%2B%282y%5E2-16y%2B32%29-10=0......factor out 5 and 2
5%28x%5E2%2B6x%2B9%29%2B2%28y%5E2-8y%2B16%29-10=0
5%28x%2B3%29%5E2%2B2%28y-4%29%5E2-10=0.......=>...h=-3 and k=4
the center: (-3,4)