Find the Rectangular-Coordinate Equation for the Parametric Equations Given $$x = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } t$$

Multiple Choice

Find the rectangular-coordinate equation for the parametric equations given. $$x = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } t$$

A) $x + y = 2,0 \leq x \leq 2$
B) $x ^ { 2 } + y ^ { 2 } = 4 , \quad 0 \leq x \leq 4$
C) $2 x ^ { 2 } + 2 y ^ { 2 } = 1 , \quad 0 \leq x \leq 2$
D) $x ^ { 2 } + y ^ { 2 } = 2 , \quad 0 \leq x \leq 2$
E) $x ^ { 2 } - y ^ { 2 } = 4$