SOLUTION: PLEASE ANSWER ASAP!!!! Points A and B are on a parabola y = 4x^2+ 7x -1 and the origin is the midpoint of AB. ***What is the length of AB? THANK YOU!!!

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: PLEASE ANSWER ASAP!!!! Points A and B are on a parabola y = 4x^2+ 7x -1 and the origin is the midpoint of AB. ***What is the length of AB? THANK YOU!!!      Log On


   

Question 11671: PLEASE ANSWER ASAP!!!!
Points A and B are on a parabola y = 4x^2+ 7x -1 and the origin is the midpoint of AB.
***What is the length of AB?
THANK YOU!!!
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let A = (xo,yo) ,B = (x1,y1),then their midpoint is
((xo+x1)/2,(yo+y1)/2) = (0,0).
So x1=-x0,y1=-yo.

Since A,B are both on the the parabola,
we have yo = +4xo%5E2%2B+7xo+-1...(1) and
-yo = 4xo%5E2-+7xo+-1...(2)

(1)+(2): 0 = +8x0%5E2+-2
So, xo = 1/2 or -1/2
and hence,yo = 4(1/4) - 7/2 - 1= -7/2
or yo = 7/2

Let O be the origin.
We see that the length of AB = 2 distance of OA
= 2++sqrt%28%281%2F2%29%5E2+%2B+%287%2F2%29%5E2%29+
= 2 +sqrt%2850%29%2F2
= +sqrt%2850%29
Kenny