Equation of Circle

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 of a circle from its equation?

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is given by the point (h, k).

Front

What is the radius of a circle?

Back

The radius of a circle is the distance from the center to any point on the circle.

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is half of the diameter, so the radius is 6.

Front

How do you calculate the radius from the equation of a circle?

Back

The radius can be calculated as the square root of the value on the right side of the equation in standard form: (x - h)² + (y - k)² = r².

Front

What is the center of a circle with endpoints of a diameter at (-11, -7) and (3, 5)?

Back

The center is found by averaging the x-coordinates and y-coordinates: Center = ((-11 + 3)/2, (-7 + 5)/2) = (-4, -1).

Front

What does the equation (x - 5)² + (y + 7)² = 8 represent?

Back

This equation represents a circle with center (5, -7) and radius √8 or 2√2.

Front

How do you convert the diameter of a circle to radius?

Back

To convert diameter to radius, divide the diameter by 2.

Front

What is the significance of the values h and k in the circle equation?

Back

The values h and k represent the x and y coordinates of the center of the circle, respectively.

Front

What is the equation of a circle with center (7, 0) and radius 3?

Back

The equation is (x - 7)² + y² = 9.