A circle has equation (x + 2)^2 + (y + 3)^2 = 4 and a line has equation 5y − 4x + 10 = 0.
(a) What is the distance from the center of the circle to the line?
(b) What is the greatest distance from a point on the circle to the line?
+128408 The center of the circle is (-2,-3) and the radius = 2
(a) We can use the formula for the distance from a point to a line to find this
D = l -4(-2)+ 5(-3) + 10 ] l 3 l
___________________ = ________ units ≈ .469 units
sqrt ( 4^2 + 5^2) sqrt (41)
(b) The greatest distance from a point on the cirlcle to this line = answer to (a) + radius ≈
.469 + 2 = 2.469
