The correct option is A A constant
y2=ax2+bx+c .......... (1)
Differentiate w.r.t x
2yy1=2ax+b .......... (2)
Here, y1=dydx
Again, diff w.r.t to x
2y21+2yy2=2a
y21+yy2=a ............. (3)
⇒y2y21+y3y2=a(ax2+bx+c) using (2)
⇒(ax+b2)2+y3y2=a2x2+abx+ac
⇒a2x2+abx+b24+y3y2=a2x2+abx+ac
⇒y3y2=ac−b24
y3y2=4ac−b24 is a constant.