A circle centered at the origin is tangent to the line 2x - y + 4 = 0. What is the area of the circle?
This boils down to finding the distance from the origin (0,0) to the line
distance = l 2(0) - 1(0) + 4 l 4
________________ = ______ = the radius of the circle
sqrt [ 2^2 +1^2 ] sqrt (5)
The area of the circle = pi (4/ sqrt (5) )^2 = (16/5)pi units^2
Here's a graph : https://www.desmos.com/calculator/6d3n0brtjx