11-4 Circles on Coordinate Plane

Front

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

Back

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

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

Back

The radius is the square root of the value on the right side of the equation (x - h)² + (y - k)² = r².

Front

What is the center of the circle in the equation (x - 3)² + (y + 4)² = 121?

Back

The center is (3, -4).

Front

What is the radius of the circle in the equation (x - 3)² + (y + 4)² = 121?

Back

The radius is 11.

Front

What does the equation (x + 1)² + (y + 1)² = 9 represent?

Back

A circle with center (-1, -1) and radius 3.

Front

How can you determine if a point lies inside, on, or outside a circle?

Back

Calculate the distance from the point to the center and compare it to the radius.

Front

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

Back

x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.

Front

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

Back

It determines the size of the circle; larger radius means a larger circle.

Front

How do you convert the general form of a circle's equation to standard form?

Back

Complete the square for x and y terms.

Front

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

Back

x² + y² = 25.