Equations and Graphs of Circles 2024

Front

What is the standard equation of a circle?

Back

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

Front

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

Back

To find the radius of a circle from its equation in the form (x - h)² + (y - k)² = r², take the square root of r².

Front

What is the center of the circle in the equation (x - 3)² + (y + 2)² = 16?

Back

The center of the circle is (3, -2).

Front

What does the term 'radius' refer to in a circle?

Back

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

Front

If the equation of a circle is (x + 1)² + (y - 4)² = 9, what is the radius?

Back

The radius is 3, since √9 = 3.

Front

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

Back

The equation is x² + y² = 25.

Front

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

Back

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

Front

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

Back

The radius is 6, since √36 = 6.

Front

What is the equation of a circle with center (-5, 7) and radius 5?

Back

The equation is (x + 5)² + (y - 7)² = 25.

Front

In the equation (x - 3)² + (y - 2)² = 16, what does 16 represent?

Back

16 represents the square of the radius of the circle.