Equation of a Circle

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

(x - h)² + (y - k)² = r²

Front

What does the variable 'r' represent in the equation of a circle?

Back

The radius of the circle.

Front

How do you find the center of a circle from its equation?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What is the radius of a circle if its equation is (x - 3)² + (y + 2)² = 16?

Back

The radius is 4, since r² = 16.

Front

What is the equation of a circle with center (0, 0) and radius 5?

Back

x² + y² = 25.

Front

If a circle has a diameter with endpoints at (2, 3) and (6, 7), what is its center?

Back

The center is (4, 5).

Front

What is the radius of a circle with the equation (x + 1)² + (y - 4)² = 9?

Back

The radius is 3, since r² = 9.

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 equation of a circle with center (-2, 1) and radius 2?

Back

(x + 2)² + (y - 1)² = 4.

Front

What is the distance formula used to find the radius of a circle given two endpoints of a diameter?

Back

Radius = 1/2 * √[(x2 - x1)² + (y2 - y1)²].