The correct option is D b2c=4a3
Let one end of the focal chord be (at2,2at), then the length of the that chord is
c=a(t+1t)2⋯(1)
Now equation of the focal chord will be
y−0=(2at−0at2−a)(x−a)
As we know that vertex coordinates of the parabola is (0,0)
Hence perpendicular distance from origin to the chord will be
b=∣∣∣−2att2−1∣∣∣√1+4t2(t2−1)2=|2at|t2+1⋯(2)
from (1)×(2)2, t will get eliminated and we get
b2c=4a3