A circle has the equaton (x-2)^2+(y+3)^2=4 and a line has the equation 5y-4x+20=0.
a) What is the distance from the center of the circel to the line.
b) What is the greatest distance from a point on the circle to the line?
Thanks!
+9519 a)
Center = (2, -3).
Using the point-line distance formula:
\(\quad \text{Distance between }(x_0, y_0)\text{ and the line }ax+by+c=0\\ = \dfrac{\left|ax_0 + by_0 + c\right|}{\sqrt{a^2 + b^2}}\)
Plugging in \((x_0, y_0, a, b, c) = (2, -3, -4, 5, 20)\) gives the answer.
b)
In this case, you plot a straight line perpendicular to 5y - 4x + 20 = 0, which passes through the center of the circle. This straight line intersects the circle twice. For each intersection, calculate the point-line distance between the intersection and the straight line 5y - 4x + 20 = 0. The smaller one is the minimum distance, and the larger one is the required answer.
