Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \frac { 1 } { 4 x ^ { 2 } + 5 y ^ { 2 } }$$

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \frac { 1 } { 4 x ^ { 2 } + 5 y ^ { 2 } }$$

A) Domain: all points in the $x y$ -plane except $( 0,0 )$ ; range: all real numbers; level curves; ellipses $4 x ^ { 2 } + 5 y ^ { 2 } = c$
B) Domain: all points in the xy-plane except $( 0,0 )$ ; range: real numbers $> 0$ ; level curves: ellipses $4 x ^ { 2 } + 5 y ^ { 2 } = c$
C) Domain: all points in the $x y$ -plane; range: all real numbers; level curves; ellipses $4 x ^ { 2 } + 5 y ^ { 2 } = c$
D) Domain: all points in the $x y$ -plane; range: real numbers $> 0$ ; level curves: ellipses $4 x ^ { 2 } + 5 y ^ { 2 } = c$