SOLUTION: Find the center and radius of the circle described by the given equation. Then find the relation's domain and range. (Hint: Graphing will help to find the domain and range.) (x

Algebra ->  Circles -> SOLUTION: Find the center and radius of the circle described by the given equation. Then find the relation's domain and range. (Hint: Graphing will help to find the domain and range.) (x      Log On


   

Question 997376: Find the center and radius of the circle described by the given equation. Then find the relation's domain and range. (Hint: Graphing will help to find the domain and range.)
(x-2)^2 + (y + 7)^2 = 36

The domain is ???.
The range is ???.
Found 2 solutions by addingup, MathLover1:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!

You can go here and graph your equation:
https://www.desmos.com/calculator

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-2%29%5E2+%2B+%28y+%2B+7%29%5E2+=+36+=> compare to %28x-h%29%5E2+%2B+%28y+-k%29%5E2+=+r%5E2+ and you see that h=2,k=-7, and r=6
so,
the center is at: (2, -7)
radius r=+6



The domain is the x value of the center +/- the radius.

2+-+6+%3C+x+%3C+2+%2B+6
-4+%3C+x+%3C+8
2+%2B6+%3C+x+%3C+2+-6
8+%3C+x+%3C+-4....which is actually same as -4+%3C+x+%3C+8

The range is the y value of the center +/- the radius.
Range:
-7+-+6%3C+y+%3C+-7+%2B+6
-13+%3C+y+%3C+-1+
-7+%2B+6%3C+y+%3C+-7-6
-1+%3C+y+%3C+-13+=>same as -13+%3C+y+%3C+-1+
so,
Domain:-4+%3C+x+%3C+8
Range:-13+%3C+y+%3C+-1+