The correct option is B a parabola
x=at2,y=2at
Eliminating the parameter t,
t=y2α⇒x=a(y2a)2⇒y2=4ax⇒y2−4ax=0
Comparing with ax2+2hxy+by2+2gx+2fy+c=0
a=0,b=1,c=f=h=0,g=−2a
∴△=∣∣
∣∣00−2a010−2a00∣∣
∣∣=−4a2≠0
Also, h2−ab=0
Hence, given curve represents a parabola.