SOLUTION: Classify the conic section: 1. x^2 + y^2 = 36 A point B ellipse C circle D hyperbola E parabol F line I think the answer is b,but i just want to make sure thats right?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Classify the conic section: 1. x^2 + y^2 = 36 A point B ellipse C circle D hyperbola E parabol F line I think the answer is b,but i just want to make sure thats right?      Log On


   

Question 161954: Classify the conic section:
1. x^2 + y^2 = 36
A point
B ellipse
C circle
D hyperbola
E parabol
F line
I think the answer is b,but i just want to make sure thats right? Thank you for your help!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+y%5E2+=+36 Start with the given equation


%28x-0%29%5E2+%2B+%28y-0%29%5E2+=+36 Replace "x" with "x-0" and replace "y" with "y-0".


%28x-0%29%5E2+%2B+%28y-0%29%5E2+=+6%5E2 Rewrite 36 as 6%5E2

Since the equation above fits the equation %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 (which is the equation of any circle) where h=0, k=0 and r=6, this shows us that the equation x%5E2+%2B+y%5E2+=+36 is a circle.



Note: if you aren't entirely sure, solve for "y" and you should get a good idea of the conic section (this isn't foolproof)