Equation of a Circle Investigation
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?
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?
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?
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?
Q5. Examine the equations above.
What happens to the radius in the equation? Change the radius a few times more to verify your answer.
Q6. Move the center of the circle to ( 6, 0) and change the radius to 3.
What is the new circle equation?
Q7. Move the center of the circle to ( -2, 0) and leave the radius to 3.
What is the new circle equation?
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?
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?
Q10. Examine the equations.
What happened to the equation when the y coordinate of the center is positive? How about when it is negative?
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.