The circle centered at (2, -1) and with radius 4 intersects the circle centered at (2, 5) and with radius sqrt(10) at two points A and B. Find (AB)^2.
+128474 We have this
(x - 2)^2 + ( y + 1)^2 = 16
(x - 2)^2 + ( y - 5)^2 = 10 subtract the second equation form the first
(y + 1)^2 - ( y - 5)^2 = 6 simplify
y^2 + 2y + 1 - y^2 + 10y - 25 = 6
12y - 24 = 6
12y = 30
y = 30 /12 = 2.5 = 5/2
Using either equation we can find x as follows
(x - 2)^2 + ( 2.5 + 1)^2 = 16
(x - 2)^2 + 12.25 = 16
(x - 2)^2 = 16 -12.25
(x -2)^2 = 15/4 take both roots
x - 2 = sqrt (15)/2 x - 2 = -sqrt (15) /2
x = sqrt (15) / 2 + 2 x = 2 - sqrt (15) /2
x= [ 4 + sqrt (15) ] /2 x= [4 -sqrt (15)] / 2
A = ( [4 + sqrt (15) ] / 2 , 5/2 )
B = ( [4 - sqrt (15) ] / 2 , 5/2 )
My question is..... What is AB supposed to represent ????
