Given an Ellipse with Major Axis of Length 2a and Minor

Given an ellipse with major axis of length 2a and minor axis of length 2b, the area is given by A =ab.
The perimeter is approximated by $$P \approx \pi \sqrt { 2 \left( a ^ { 2 } + b ^ { 2 } \right) }$$ a. Determine the area of the ellipse. b. Approximate the perimeter.
- $$\frac { x ^ { 2 } } { 4 } + \frac { ( y - 6 ) ^ { 2 } } { 12 } = 1$$

A) a. $A = 48 \pi$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units
B) a. $A = 48 \pi$ square units
b. $P \approx 12 \pi$ units
C) a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 4 \pi \sqrt { 2 }$ units
D) a. $A = 4 \pi \sqrt { 3 }$ square units
b. $P \approx 12 \pi$ units