In the graph below, what has changed about the circle?
What are the new values of h, k, and r? Click on the blank to see the correct answer.
h = Interactive button. Assistance may be required. __________ 4
k = Interactive button. Assistance may be required. __________ 3
r = Interactive button. Assistance may be required. __________ 5
How does the algebraic proof for point G (1 , -1) on the line look now?
(1 – 4)2 + (-1 – 3)2 = (5)2
(-3)2 + (-4)2 = (5)2
9 + 16 = 25
25 = 25
True again, proving point G on the circle with center (3, 4).
For whatever point you choose on a circle, you should be able to show that point is the same distance (r) from the center of the circle as any other point on the circle.
Go to the following website to further explore the changes in the equation of a circle as the graph moves: Equation of Circle.