SOLUTION: Two circles x^2+y^2=11 and (x-3)^2+y^2=2 intersect at two points. P and Q. Find the exact length of the line segment PQ.

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Two circles x^2+y^2=11 and (x-3)^2+y^2=2 intersect at two points. P and Q. Find the exact length of the line segment PQ.       Log On


   

Question 315555: Two circles x^2+y^2=11 and (x-3)^2+y^2=2 intersect at two points. P and Q. Find the exact length of the line segment PQ.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for the intersection points.
x%5E2%2By%5E2=11
y%5E2=11-x%5E2
.
.
.
%28x-3%29%5E2%2By%5E2=2
%28x-3%29%5E2%2B%2811-x%5E2%29=2
x%5E2-6x%2B9%2B11-x%5E2=2
-6x%2B20=2
-6x=-18
highlight%28x=3%29
Now solve for y
y%5E2=11-x%5E2
y%5E2=11-9
y%5E2=2
highlight%28y=0+%2B-+sqrt%282%29%29
Points P and Q are (3,-sqrt%282%29) and (3,sqrt%282%29).
The length of PQ is 2%2Asqrt%282%29.