Finding the Center and Radius of a Circle (3.4.2)

Question 1

• Completing the square:
• Reduce the equation, if there is a coefficient in front of x^2.
• Move the constant to the right.
• Complete the square

Answer 1

• Completing the square:
• Reduce the equation, if there is a coefficient in front of x^2.
• Move the constant to the right.
• Complete the square

Question 2

• Watch your signs when stating the center of the circle from the equation. The equation reads (x – h) and (y – k) so the signs change from the equation to the ordered pair notation.

Answer 2

• Watch your signs when stating the center of the circle from the equation. The equation reads (x – h) and (y – k) so the signs change from the equation to the ordered pair notation.

Question 3

Frequently you are given an equation that you think is for a circle because it has terms with both x^2 and y^2.
Try to convert the equation to your standard form for a circle by completing the square. Do the completing the square process once for the x-terms and a second time for the y-terms. Here note that 6/2 = 3 and 32 = 9. So 9 is added to the equation for the x-terms. Next work with the y-terms. You can see that 8/2 = 4, and 42 = 16. So, 16 is being added to the equation. Now write the completed squares as binomials and that gives the left side of the circle equation. The total on the right side represents the radius squared. In this form you know your center and your radius.

This example works the same way.

1. Complete the square for the x-terms.
2. Complete the square for the y-terms.
3. Write the binomials on the left side.
4. Note the center and the radius.

Answer 3

Frequently you are given an equation that you think is for a circle because it has terms with both x^2 and y^2. Try to convert the equation to your standard form for a circle by completing the square. Do the completing the square process once for the x-terms and a second time for the y-terms. Here note that 6/2 = 3 and 32 = 9. So 9 is added to the equation for the x-terms. Next work with the y-terms. You can see that 8/2 = 4, and 42 = 16. So, 16 is being added to the equation. Now write the completed squares as binomials and that gives the left side of the circle equation. The total on the right side represents the radius squared. In this form you know your center and your radius.

This example works the same way.

1. Complete the square for the x-terms.
2. Complete the square for the y-terms.
3. Write the binomials on the left side.
4. Note the center and the radius.