SOLUTION: How would you graph (x-2)^2+y^2=5 and (y+2)^2-x^2=16

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Question 205384: How would you graph (x-2)^2+y^2=5 and (y+2)^2-x^2=16
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
How to graph:
%28x-2%29%5E2%2By%5E2+=+5 and...
%28y%2B2%29%5E2-x%5E2+=+16 The basic idea is to take each of these equations and solve them for y and, for each equation, you will get two solutions which, when graphed, will show half the of the complete graph.
Here's how it would go...
%28x-2%29%5E2%2By%5E2+=+5 Subtract %28x-2%29%5E2 from both sides.
y%5E2+=+-%28x-2%29%5E2%2B5 Expand the right side.
y%5E2+=+-%28x%5E2-4x%2B4%29%2B5
y%5E2+=+-x%5E2%2B4x-4%2B5
y%5E2+=+-x%5E2%2B4x%2B1 Now take the square root of both sides.
y+=+sqrt%28-x%5E2%2B4x%2B1%29 and y+=+-sqrt%28-x%5E2%2B4x%2B1%29 Now graph these two equations using your graphing utility (also known as graphing calculator).

Similarly for the second equation:
%28y%2B2%29%5E2-x%5E2+=+16 Add x%5E2 to both sides.
%28y%2B2%29%5E2+=+x%5E2%2B16 Take the square root of both sides.
y%2B2+=+sqrt%28x%5E2%2B16%29 and y%2B2+=+-sqrt%28x%5E2%2B16%29 Now subtract 2 from both sides of each of the solutions.
y+=+sqrt%28x%5E2%2B16%29-2 and y+=+-sqrt%28x%5E2%2B16%29-2 Now graph these as before: