Exploration of a Circle
The general form of a circle is as follows:
Go to the following link and complete the questions below.
http://www.sasked.gov.sk.ca/docs/math30/conics/conics/laboratory/circlehk.html
At any point, to start over, click REFRESH on your browser
1.
Change the value of h to 2. In what direction does the circle move?
2.
Change the value of h to -3. In what direction does the circle move?
3.
Change the value of k to 2. In what direction does the circle move?
4.
Change the value of k to -3. In what direction does the circle move?
5.
Change the value of r, what happens to the circle?
6.
Create a circle with a center of (3,5) and a radius of 2. What is the equation of the circle?
7.
Create a circle with a center of (-2, 3) and a radius of 4. What is the equation circle?
8.
Determine the center and radius of a circle with the equation as follows:
9.
Determine the center and radius of a circle with the equation as follows:
10. Summarize how h, k, and r affect the size and location of a circle.
11. Write the equations for the following circles.
a)
c)
12. Sketch the following circles on the grids given.
a)
c)
b)
d)
b)
d)
BONUS QUESTIONS
13. Find the equation of a circle that has a diameter with the endpoints given by A(0 , -2) and B(0 , 2).
Answer: center at (0, 0), radius = 2, equation: x2 + y2 = 4
14. Find the equation of the circle such that the three points A(-5 , 0), B(1 , 0) and D(-2 , -3) are on the circle.
2
2
Answer: (x + 2) + y = 9