Question

given the circle having the equation x^2+y^2=9, find the shortest distance from the point (4,5). find the longest distance from the point (4,5).

Answer 1

The points on the circle that are the nearest and farthest from (4,5) will be the two points on the line that connects (4,5) with the center of the circle, located at (0,0). The equation of that line is
y = (5/4) x

Points on both the line and the circle must satisfy the equation
x^2 + (25/16)x^2 = 9
(41/16)x^2 = 9
x = + or - 12/sqrt41 = + or - 1.87409
y = (5/4)x = + or - 2.34261
Farthest point: (-1.87409, -2.3261)
Nearest point: (1.87409, 2.3261)