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) $x ^ { 2 } - y ^ { 2 } = 4$

Question

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) $x ^ { 2 } - y ^ { 2 } = 4$

Quizplus · Accepted Answer

Using the trigonometric identity $\sin^2t + \cos^2t = 1$, we can add the given equations: $x = 2\cos^2t$ and $y = 2\sin^2t$ to get $x + y = 2( \cos^2t + \sin^2t) = 2$. The range for $x$ is $0 \leq x \leq 2$ because $2\cos^2t$ varies between 0 and 2 as $t$ changes.

Find the Rectangular-Coordinate Equation for the Parametric Equations Given x=2cos⁡2t,y=2sin⁡2tx = 2 \cos ^ { 2 } t , y = 2 \sin ^ { 2 } tx=2cos2t,y=2sin2t

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