1.A circle has equation (x − 2)2 + (y + 3)2 = 4 and a line has equation 5y − 4x + 20 = 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?
+128631 a) The center of the circle is (2, -3)
Using the formula for the distance from a point to a line, we have
l 4(2) - 5(-3) - 20 l l 3 l 3
___________________ = ______ = ________
sqrt (4^2 + 5^2) sqrt 41 sqrt (41)
b) greatest distance from a point on the circle to the line =
distance found in (a) + radius =
3 / sqrt (41) + 2
