The correct option is B Parabola
x=sin2t,y=2cost
On Squaring y
⇒y2=4cos2t
⇒cos2t=y24⋯⋯(1)
sin2t=x⋯⋯(2)
Adding (1)and (2)
x+(y2)2=1
4x+y2−4=0
On comparing with
ax2+by2+2hxy+2gx+2fy+c=0
We have , a=0,b=1,h=0,g=2,f=0,c=−4
Δ=abc+2fgh−af2−bg2−ch2=−4
and h2=ab
So, it represents a parabola