Equations of Circles Review

Front

What is the standard form of the equation of a circle?

Back

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center and radius from the standard form of a circle's equation?

Back

From the equation (x - h)² + (y - k)² = r², the center is (h, k) and the radius is r.

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

The equation is x² + y² = 25.

Front

Convert the equation x² + y² - 10x - 6y + 9 = 0 to standard form.

Back

(x - 5)² + (y - 3)² = 25.

Front

What is the radius of a circle with the equation (x + 2)² + (y - 4)² = 16?

Back

The radius is 4.

Front

Write the equation of a circle with center (3, -2) and radius 4.

Back

The equation is (x - 3)² + (y + 2)² = 16.

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for both x and y terms.

Front

What is the center of the circle given by the equation (x - 1)² + (y + 3)² = 36?

Back

The center is (1, -3).

Front

Write the equation of a circle with center (-1, 2) and radius 3.

Back

The equation is (x + 1)² + (y - 2)² = 9.

Front

Convert the equation x² + y² + 4x - 8y + 4 = 0 to standard form.

Back

(x + 2)² + (y - 4)² = 8.