A point (x,y) is a distance of 6 units from the x-axis. It is a distance of sqrt(58) units from the point (8,3). It is a distance sqrt(n) from the origin,. Given that x < 8, what is n?
Costruct a circle with a center of (8,3) and a radius of sqrt 58
The equation of this circle is
(x - 8)^2 + ( y - 3)^2 = 58
Our point must be on this circle and is 6 units from the x axis (y coord of the point = 6)
So
(x - 8)^2 + (6 -3)^2 = 58
(x - 8)^2 + 9 = 58
(x - 8)^2 = 49
x - 8 = -sqrt (49)
x = 8 - 7 = 1
n = 1^2 + 6^2 = 37