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


   

Question 161955: Classify the conic section:
x^2 - y^2 = 36
A circle
B hyperbola
C parabola
D point
E line
F ellipse

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+-+y%5E2+=+36 Start with the given equation


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


%28x-0%29%5E2%2F36+-+%28y-0%29%5E2%2F36+=+cross%2836%2F36%29 Divide EVERY term by 36 to make the right side equal to 1.


%28x-0%29%5E2%2F36+-+%28y-0%29%5E2%2F36+=+1 Reduce


%28x-0%29%5E2%2F6%5E2+-+%28y-0%29%5E2%2F6%5E2+=+1 Rewrite 36 as 6%5E2


Since the last equation follows the form %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 (which is the general equation of an hyperbola) where h=0, a=6, k=0 and b=6, this means that the equation x%5E2+-+y%5E2+=+36 is an ellipse.


So you are correct.