Circle Equations (Converting Forms)

Front

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

Back

The standard form of a circle's equation 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 of a circle from its general equation?

Back

To find the center from the general equation Ax² + Ay² + Bx + Cy + D = 0, rewrite it in standard form by completing the square for x and y.

Front

What is the radius of a circle given in general form?

Back

The radius can be found by rearranging the general form into standard form and identifying r from (x - h)² + (y - k)² = r².

Front

Convert the general equation x² + y² - 10x + 8y - 8 = 0 to standard form.

Back

(x - 5)² + (y + 4)² = 7².

Front

What is the center of the circle given by the equation x² + y² - 10x + 8y - 8 = 0?

Back

The center is (5, -4).

Front

How do you determine the radius from the equation x² + y² - 10x + 8y - 8 = 0?

Back

The radius is 7, derived from the standard form after completing the square.

Front

What is the equation of a circle with center (5, -3) and radius 9?

Back

The equation is x² + y² - 10x + 6y - 47 = 0.

Front

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

Back

Complete the square for the x and y terms, then rearrange to the form (x - h)² + (y - k)² = r².

Front

What is the radius of the circle given by the equation x² + y² - 10x + 8y - 23 = 0?

Back

The radius is 8.

Front

What does the term 'completing the square' refer to in the context of circle equations?

Back

Completing the square is a method used to rewrite a quadratic expression in the form (x - p)² + (y - q)² = r².