Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \sqrt { 25 - x ^ { 2 } - y ^ { 2 } }$$

A) Domain: all points in the $x y$ -plane satisfying $x ^ { 2 } + y ^ { 2 } = 25$ ; range: real numbers $0 \leq z \leq 5$ ; level curves: circles with centers at $( 0,0 )$ and radii $r , 0 < r \leq 5$
B) Domain: all points in the $x y$ -plane; range: real numbers $0 \leq z \leq 5$ ; level curves: circles with centers at ( 0 , 0 ) and radii $r , 0 < r \leq 5$
C) Domain: all points in the $x y$ -plane; range: all real numbers; level curves: circles with centers at $( 0,0 )$
D) Domain: all points in the $x y$ -plane satisfying $x ^ { 2 } + y ^ { 2 } \leq 25$ ; range: real numbers $0 \leq z \leq 5$ ; level curves: circles with centers at $( 0,0 )$ and radii $r , 0 < r \leq 5$