Conic Sections 1.1: Circles
Student Name:
Definition of a Circle
Graphing the Circle
The standard form of the equation of a circle with radius r and center (h, k) is
.
A graph of 
can be generated by Mathematica using the following commands. Notice that the center of the circle and the radius of the circle are printed after the graph.
Graphing a Translated Circle
If the center of the circle moves to a new point, the circle will be translated.
Finding the Radius of a Circle (Given the Center and a Point On the Circle)
If you know the center of a circle and you know at least one point on the circle, you can use the distance formula to find the radius of the circle.
Mathematica can easily help to solve this problem using the following commands.
Practice Problems
Problem 1: Eye of a Hurricane
A hurricane located at point (0,0) is causing high winds and heavy rain in a town 100 miles north and 50 miles east of the center of the hurricane.
Problem 1 Answer:
What is the distance between the hurricane center and the town?
Use the following commands to create a graph of the hurricane center and the town. (Note: You do not need to change anything in this input box, but it will not work if you have not already calculated the radius of the hurricane.)
Problem 2: The Hurricane is Moving!
The hurricane from problem one has moved due east 140 miles.
Problem 2 Answers:
Look at the new graph. Did the hurricane move closer to the town or farther away?
Calculate the distance between the new hurricane center and the town. How far away is the hurricane, in its new location?
