Q1. Move the center of circle A to the origin (0,0) and change the radius to 1. This is called the parent function of a circle.
What is the equation of this circle?
x^2 + y^2 = 1
Q2. Leave the center of circle A to the origin (0,0) and change the radius to 3.
What is the equation of this circle?
x^2 + y^2 = 9
Q3. Leave the center of circle A to the origin (0,0) and change the radius to 5.
What is the equation of this circle?
x^2 + y^2 = 25
Q4. Leave the center of circle A to the origin (0,0) and change the radius to 4.
What is the equation of this circle?
x^2 + y^2 = 16
Q5. Examine the equations above.
What happens to the radius in the equation? Change the radius a few times more to verify your answer.
The radius is squared.
Q6. Move the center of the circle to ( 6, 0) and change the radius to 3.
What is the new circle equation?
(x -6)^2 + y^2 = 9
Q7. Move the center of the circle to ( -2, 0) and leave the radius to 3.
What is the new circle equation?
(x + 2)^2 + y^2 = 9
Q8. Examine the equations above.
What happened to the equation when the x coordinate of the center is positive? How about when it is negative?
If x is positive it is subtracted from the x if it is negative it is added to the x.
Q9. Move the center of the circle to ( 0, 3) and leave the radius to 3. Write the equation. Then move the center of the circle to ( 0, -5) and leave the radius to 3.
What are the two new equations?
x^2 + (y - 3)^2 = 9[br]x^2 + (y + 5)^2 = 9
Q10. Examine the equations.
What happened to the equation when the y coordinate of the center is positive? How about when it is negative?
If y is positive it is subtracted from the y. if it is negative it is added to the y.
Q11. The general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
Write the equation of a circle with a center at ( -3, 4) and a radius of 8.