SOLUTION: the line x+3y=1 intersects the curve 5y=20-3x-x^2 at point P & Q. calculae the length of PQ

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Question 944734: the line x+3y=1 intersects the curve 5y=20-3x-x^2 at point P & Q. calculae the length of PQ
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3y=1
x=1-3y
Substitute,
5y=20-3%281-3y%29-%281-3y%29%5E2
5y=20-3%2B9y-%281-6y%2B9y%5E2%29
5y=20-3%2B9y-1%2B6y-9y%5E2
5y=16%2B15y-9y%5E2
-9y%5E2%2B10y%2B16=0
-%28y-2%29%289y%2B8%29=0
So then,
y-2=0
y=2
and
9y%2B8=0
9y=-8
y=-8%2F9
Solving for x in each case,
x=1-3%282%29=1-6=-5
and
x=1-3%28-8%2F9%29=1%2B24%2F9=33%2F9=11%2F3
So the two intersection points are
(-5,2) and (11/3,-8/9)
Use the distance formula,
D%5E2=%28-5-11%2F3%29%5E2%2B%282-%28-8%2F9%29%29%5E2
D%5E2=%28-15%2F3-11%2F3%29%5E2%2B%2818%2F9%2B8%2F9%29%5E2
D%5E2=%28-26%2F3%29%5E2%2B%2826%2F9%29%5E2
D%5E2=%28676%2F9%29%2B%28676%2F81%29
D%5E2=%286084%2F81%29%2B%28676%2F81%29
D%5E2=6760%2F81
highlight%28D=%2826sqrt%2810%29%29%2F9%29