Write the standard form of the equation of the circle with center (-5, 2) and radius 4. What is the domain and range?

We'll recall what is the standard form of the equation of
circle:

(x-h)^2 + (y-k)^2 = r^2, where the coordinates of
the center of circle are represented by the pair (h,k) and r is the radius of the
circle:

The standard form of the equation of circle
is:

(x +5 )^2 + (y - 2)^2 =
4^2

The domain of the definition consists of all x values
that makes the equation possible:

(x +5 )^2 =
4^2

We'll take square root both
sides:

x + 5 = 4 => x =
-1

x + 5 = -4 => x =
-9

The domain of definition of the function is [-9 ;
-1].

The range of the values of function
is:

(y - 2)^2 = 4^2

y - 2 = 4
=> y = 6

y - 2 = -4 => y =
-2

The range of the values of function is [-2 ;
6].

Therefore, the requested standard form of
the equation of circle andthe domain and the range of the function are: (x +5 )^2 + (y -
2)^2 = 4^2 ; domain [-9 ; -1] and the range [-2 ;
6].