The correct option is C An ellipse
x=5cost,y=2sint
cost=x5⋯⋯(1)
sint=y2⋯⋯(2)
Squaring (1) and (2) and then adding both
(x5)2+(y2)2=1
x225+y24=1
4x2+25y2−100=0
On comparing with
ax2+by2+2hxy+2gx+2fy+c=0
We have a=4,b=25,h=0,g=0,f=0,c=−100
Δ=abc+2fgh−af2−bg2−ch2=−10000≠0
and h2<ab
So, its an ellipse.