SOLUTION: How would you graph the hyperbola {{{x^2 - y^2 = 4}}}?? And does the center of the hyperbola HAVE to be on (0,0)? Because I worked it out the best that I could, and I got the ce

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How would you graph the hyperbola {{{x^2 - y^2 = 4}}}?? And does the center of the hyperbola HAVE to be on (0,0)? Because I worked it out the best that I could, and I got the ce      Log On


   

Question 90317This question is from textbook Elementary and Intermediate Algebra
: How would you graph the hyperbola x%5E2+-+y%5E2+=+4??
And does the center of the hyperbola HAVE to be on (0,0)? Because I worked it out the best that I could, and I got the center at (2,0) I'm thinking that I did something wrong, though. Could you please help? Thanks This question is from textbook Elementary and Intermediate Algebra

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The x-intercepts are at (2,0), (-2,0)
The center (which is not a point on the hyperbola) is (0,0)
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-y%5E2+=+4
Write your equation in the standard form for a hyperbola with the center at (0, 0) and the vertices on the x-axis.: %28x%5E2%2Fa%5E2%29-%28y%5E2%2Fb%5E2%29+=+1
x%5E2-y%5E2+=+4 Divide both sides by 4.
%28x%5E2%2F4%29-y%5E2%2F4%29+=+1 Rewrite as:
%28x%5E2%2F2%5E2%29-%28y%5E2%2F2%5E2%29+=+1
Let's see what the graph looks like!
graph%28600%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28x%5E2-4%29%2C-sqrt%28x%5E2-4%29%2Cx%2C-x%29
The center is at (0, 0) and the assymptotes are:
y+=+%28a%2Fb%29x and y+=+-%28a%2Fb%29x or, in this case:
y+=+x and y+=+-x