SOLUTION: find the coordinates of the midpoint of the chord in the line x+2y-1=0 which intersects the ellipse x^2+2y^2=3

Question 722492: find the coordinates of the midpoint of the chord in the line x+2y-1=0 which intersects the ellipse x^2+2y^2=3
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the coordinates of the midpoint of the chord in the line x+2y-1=0 which intersects the ellipse x^2+2y^2=3
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x+2y-1=0
x^2+2y^2=3
..
x=(-2y+1)
(-2y+1)^2+2y^2=3
4y^2-4y+1+2y^2-3=0
6y^2-4y-2=0
3y^2-2y-1=0
(3y+1)(y-1)=0
y=-1/3
x=2/3+1=5/3
or
y=1
x=-2+1=-1
points of intersection: (5/3,-1/3) and (-1,1)
midpoint coordinates of chord: (-1+5/3)/2, (1-1/3)/2=(1/3,1/3)
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