Hello, can someone help me answer this question? Thanks in advance
Points A and B are on the curve y= (4x^2)+7x-1, and (0,0) is the midpoint of the line segment AB. Find the length of AB.
y=4x^2+7x-1
let coordinates of A be (x1,y1)
coordinates of B be (x2,y2)
since (0,0) is the midpoint of line segment AB therfor
(x1+x2)/2=0
x1=-x2
similarly y1=-y2
now according to the equation
y1^2=4(x1)^2+7x1-1 and
y2^2=4(x2)^2+7x2-1
since y1=-y2 therefor
4(x1)^2+7x1-1 +4(x2)^2+7x2-1 =0
now after putting x1=-x2 we get
8(x2)^2=2 therefor
x2=+-(1/2)
let x2=(1/2) so x1=(-1/2)
put these value in equation and obtain value of y1 and y2
so A=(-1/2,-7/2) and B=(1/2,7/2)
using distance formula we get distance between them=sqrt[50]