A point (x, y) is a distance of 6 units from the x-axis. It is a distance of 5 units from the point (8, 3). It is a distance \sqrt(n) from the origin. Given that x<8, what is n?
+128408 Using the Pythgorean Theorem the point can be represented as :
[x, y ] = [sqrt (n - 6^2), 6 ]
So we have that the distance from (x,y) to (8,3) = 5 units....so......
[ sqrt (n - 6^2) - 8]^2 + [ 6 -3]^2 = 25 simplify
(n - 36) - 16sqrt(n - 36) + 64 + 9 = 25
n - 36 + 73 - 25 = 16sqrt(n - 36)
n + 12 = 16sqrt(n - 36) square both sides
n^2 + 24n + 144 = 256n - 9216
n^2 - 232n + 9360 = 0 factor as
(n - 52) (n - 180) = 0
If n = 52 then x = sqrt (52 - 36) = sqrt(16) = 4
If n = 180 then x = sqrt (180 - 36) = sqrt (144) = 12
So (x , y ) = ( 4, 6)
And n = 52
Here's a graph
Corrected Answer!!!
