9-3 Circles in the Coordinate Plane

Front

What is the standard form of the equation of a circle in the coordinate plane?

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 determine the radius from the equation of a circle?

Back

The radius can be determined from the equation (x - h)² + (y - k)² = r² by taking the square root of r².

Front

What is the center of the circle in the equation (x + 2)² + (y - 4)² = 25?

Back

The center of the circle is (-2, 4).

Front

If the radius of a circle is 7, what is the equation of the circle centered at (1, -3)?

Back

The equation of the circle is (x - 1)² + (y + 3)² = 49.

Front

What does the term 'diameter' refer to in relation to a circle?

Back

The diameter is the distance across the circle through its center, equal to twice the radius.

Front

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

Back

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

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

What is the equation of a circle with center at the origin and radius 4?

Back

The equation of the circle is x² + y² = 16.

Front

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

Back

The center can be found from the equation (x - h)² + (y - k)² = r² by identifying the values of h and k.

Front

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

Back

The variable 'r' represents the radius of the circle.