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Question 470222: The straight line meets the curve  at the points A and B. Find the length of AB, correct to one decimal place.
*Please answer as soon as possible bro :) =)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! The straight line,5y+2x=1, meets the curve,xy+24=0, at the points A and B. Find the length of AB, correct to one decimal place.
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5y+2x=1
5y=-2x+1
y=-2x/5+1/5
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xy+24=0
y=-24/x
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-2x/5+1/5=-24/x
LCD:5x
-2x^2+x=-120
2x^2-x-120=0
solve with quadratic formula:
a=2, b=-1, c=-120
x=[-(-1)ħsqrt(1-4*2*-120)]/2*2
x=[1ħ√961]/4
x=(1ħ31)/4=32/4=8
y=-24/x=-24/8=-3
or
x=-30/4=-7.5
y=-24/x=-24/-7.5=3.2
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Points of intersection:A, (8,-3) and B, (-7.5,3.2)
Using distance formula to find length AB:
d^2=(x1-x2)^2+(y1-y2)^2
AB^2=(8-(-7.5))^2+(-3-3.2)^2
........=(15.5)^2+(-6.2)^2
........=240.25+38.44=278.69
AB=√278.69=16.7
See graph below as a visual check on the answers
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