The correct option is B Ellipse
As given that A lies on line y=2x and B on the line y=x
Let A(t,2t) and B(k,k); AB=4
√(t−k)2+(2t−k)2=4
⇒(t−k)2+(2t−k)2=16 …(1)
and let mid point of AB be (x,y)
t+k2=x,k+2t2=y
⇒t=2(y−x),k=4x−2y
By equation (1)
(4y−6x)2+(6y−8x)2=16
⇒(2y−3x)2+(3y−4x)2=4
⇒25x2+13y2−36xy−4=0
⇒△=∣∣
∣∣ahghbfgfc∣∣
∣∣
⇒△=∣∣
∣∣25−180−1813000−4∣∣
∣∣
⇒△≠0
and
h2<ab So, it's an ellipse