Given that a and B are nonzero vectors and the function f (x) = (XA + b) (a-xb), a necessary and insufficient condition for the image of F (x) to be a parabola symmetric about the y-axis is A.a⊥b B. A parallel B C.|a|=|b| D.a=b

Given that a and B are nonzero vectors and the function f (x) = (XA + b) (a-xb), a necessary and insufficient condition for the image of F (x) to be a parabola symmetric about the y-axis is A.a⊥b B. A parallel B C.|a|=|b| D.a=b

f(x)=(xa+b)(a-xb)=-ab*x^2+(a^2-b^2)*x+ab,
The image of F (x) is symmetric about the Y axis,
So a ^ 2-B ^ 2 = 0,
So | a | = | B |
Choose C

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