Topic 9-1: Graphing Circles

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 identify 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 does the radius of a circle represent in its equation?

Back

The radius of a circle in the equation (x-h)² + (y-k)² = r² is represented by r, which is the distance from the center to any point on the circle.

Front

Given the equation (x-2)² + (y+3)² = 25, what is the center and radius of the circle?

Back

Center: (2, -3), Radius: 5.

Front

What is the equation of a circle with center (0, 0) and radius 4?

Back

The equation is x² + y² = 16.

Front

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

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for x and y.

Front

What is the significance of the value on the right side of the equation (x-h)² + (y-k)² = r²?

Back

The value on the right side (r²) represents the square of the radius of the circle.

Front

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

Back

The radius is 3.

Front

What is the center of the circle described by the equation (x-5)² + (y+2)² = 16?

Back

The center is (5, -2).

Front

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

Back

The radius can be found by taking the square root of the value on the right side of the equation in standard form.