SOLUTION: Classify the conic section x^2 + y^2 = 121 A hyperbola B ellipse C point D circle E parabola F line I believe the answer is B. But I am not 100% sure, and Id love

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Classify the conic section x^2 + y^2 = 121 A hyperbola B ellipse C point D circle E parabola F line I believe the answer is B. But I am not 100% sure, and Id love       Log On


   

Question 161957: Classify the conic section
x^2 + y^2 = 121
A hyperbola
B ellipse
C point
D circle
E parabola
F line

I believe the answer is B. But I am not 100% sure, and Id love to know if that is correct, and if not, what is? Thank you so much for your time.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!




The equation x%5E2+%2B+y%5E2+=+121 could be rewritten as %28x-0%29%5E2+%2B+%28y-0%29%5E2+=+121 (since adding/subtracting 0 doesn't affect the equation).

Also, take note that 11%5E2=121. So this also means that %28x-0%29%5E2+%2B+%28y-0%29%5E2+=+121 further becomes %28x-0%29%5E2+%2B+%28y-0%29%5E2+=+11%5E2


Remember, the formula for any circle is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 where the center is at (h,k) and the radius is "r". Since the equation above fits this format, this shows us that the equation x%5E2+%2B+y%5E2+=+121 is a circle



Note: if you aren't entirely sure, solve for "y" and graph to get a visual clue (however, this won't fully confirm it every time)