Write the equation in graphing form of each circle described below.

1. A circle with radius $12$ centered at the point $(–2, 13)$.

   Hint (a):

   $(x − h)^2 + (y − k)^2 = r^2$

   Answer (a):

   $(x + 2)^2 +(y \ – \ 13)^2 = 144$

2. A circle with center $(–1, –4)$ and radius $1$.

   Hint (b):

   Refer to the hint in part (a).

3. A circle with equation $x^2 + y^2 – 6x + 16y + 57 = 0$. (Hint: Complete the square for both $x$ and $y$.)

   Step 1(c):

   $(x^2-6x+?)+(y^2+16y+?)=-57$

    Step 2(c):

   $(x^2-6x+9)+(y^2+16y+64)=-57+9+64$

    Step 3(c):

   Factor the expressions in parentheses and simplify.