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 and radius from the general form of a circle's equation?

Back

To find the center and radius from the general form Ax² + Ay² + Bx + Cy + D = 0, rearrange to standard form by completing the square.

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

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

Back

The radius is 7.

Front

Convert the general form of the circle x² + y² + 6x - 12y + 20 = 0 to standard form.

Back

The standard form is (x + 3)² + (y - 6)² = 25.

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 completing the square involve when converting to standard form?

Back

Completing the square involves rearranging the equation and adding/subtracting terms to form perfect squares.

Front

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

Back

The general form is Ax² + Ay² + Bx + Cy + D = 0.

Front

How do you identify the center from the standard form of a circle's equation?

Back

The center (h, k) can be identified directly from the standard form (x - h)² + (y - k)² = r².

Front

What is the significance of the radius in a circle's equation?

Back

The radius determines the size of the circle and is the distance from the center to any point on the circle.