Under the Transformation X = U + V, Y = $x ^ { 2 } + y ^ { 2 } \leq 1$

Multiple Choice

Under the transformation x = u + v, y = v - 2u, the image of the circle $x ^ { 2 } + y ^ { 2 } \leq 1$ is an ellipse. What is the area of that ellipse?

A) $\frac { \pi } { 4 }$

B) $\frac { \pi } { 3 }$
C) $\frac { \pi } { 2 }$
D) $\frac { 2 \pi } { 3 }$
E) $\pi$
F) $\frac { 3 \pi } { 2 }$

G) $2 \pi$

H) $3 \pi$