A circle centered at the origin is tangent to the line 2x-y+4=0. What is the area of the circle?
+128408 2x - y + 4 = 0
This boils down to finding the distance between the origin and this line
This is given by
l 2(0) - 0 + 4 l 4
_____________ = ______ = the radius of the circle
sqrt (2^2 + 1^2) sqrt (5)
Area of circle = pi * radius^2 = pi *(4/sqrt(5) )^2 = (16/5)pi units^2
Here's the graph to show this : https://www.desmos.com/calculator/xlkqr2a40h
