Consider the equation $\left(x − 2\right)^{2} + \left(y + 7\right)^{2} = 81$.

1. What is the shape of the graph? How can you tell?

   Hint (a):

   What family of equations does this look like?

   Answer (a):

   A circle looks like the family $\left(x − h\right)^{2}+\left(y − k\right)^{2} = r ^{2}$.

2. What other information can you get about the graph by looking at the equation?

   Hint (b):

   What is the center of the circle? What is the value of the radius?

3. Graph the equation without a table. Is the relation a function? Why or why not?

   Hint (c):

   To graph a circle, all you need to know is its center point and its radius. How do you find these?

   Hint 2 (c):

   In this case, the center of the circle is not at the origin. The center of the circle will be moved two to the right and seven down, located at the point (2, −7). The radius, in this case, is the square root of 81.

   More Help (c):

   What is the definition of a function? Is this graph consistent with the definition?