Which equation includes?

Question

Which equation includes the curve defined parametrically by x(t)=cos^2 (t) and y(t)=2 sin(t)?

 

a) x^2+y^2=4

 

b) x^2+y^2=1

 

c) 4x^2+y^2=4

 

d) 4x+y^2=4

 

e) x+4y^2=1

 

Answer: D. 

 

Show your work.

Answer 1

d.  Let  x=cos²t  and  y=2sint

y/2= sint 

(y/2)²=sin²t

1-(y/2)²=1-sin²t=cos²t=x

1-y²/4=x

4-y²=4x or 4x+y²=4

Answer 2

X( t) = Cos^2 t

 

Y ( t) = 2 Sin t

 

   (y/2 ) ^2 = Sin^2t

 

    X + + 4y^2 = Cos ^2t + Sin^2 t = 1

 

    D is the correct answer.