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?

Guest Sep 25, 2019

#1**+1 **

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!!!**

CPhill Sep 25, 2019