Find the Absolute Maximum and Minimum Values of the Function $f ( x , y ) = x y ;$

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
-Function: $f ( x , y ) = x y ;$ curve: $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } = 1 , y \geq 0$ . (Use the parametric equations $x = 6 \cos t , y = 9 \sin t$ .)

A) Absolute maximum: $\frac { 27 } { 2 }$ at $t = \frac { \pi } { 4 } ;$ absolute minimum: $- \frac { 27 } { 2 }$ at $t = \frac { 3 \pi } { 4 }$
B) Absolute maximum: $\frac { 27 } { 2 }$ at $t = \frac { \pi } { 4 }$ ; absolute minimum: $- 27$ at $t = \frac { 3 \pi } { 4 }$
C) Absolute maximum: 27 at $t = \frac { \pi } { 4 } ;$ absolute minimum: $- \frac { 27 } { 2 }$ at $t = \frac { 3 \pi } { 4 }$
D) Absolute maximum: 27 at $t = \frac { \pi } { 4 } ;$ absolute minimum: $- 27$ at $t = \frac { 3 \pi } { 4 }$