Question

Give the center, radius, and equation of the circle in the graph.

Answer 1

`(x-2)^2+(y+3)^2=4`

Explanation:

• A circle's equation consist on the following expression:
  `(x-a)^2+(y-b)^2=r^2`, where r is the magnitude of the radio, and (a,b) are the coordenates of the center of the circle.
• In this case, a=2 and b= - 3, because the circle is centered in (x,y)=(2, - 3).
• The radio, which is the distance between the center of the radio to any point in its border, equals r=2 (because of the scale of the graphic, in this case two squares of the grid equal 2 units, then r=2).
• Finally, using the previous information to replace in the equation
  `(x-2)^2+(y+3)^2=4`, where the fact that r=2 and
  `2^2=4` was used.