Circle Equations Review

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 of the circle and r is the radius.

Front

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

Back

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

Front

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

Back

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

Front

If the equation of a circle is (x + 3)² + (y - 4)² = 16, what is the center and radius?

Back

The center is (-3, 4) and the radius is 4.

Front

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

Back

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

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 of the equation represents the square of the radius (r²) of the circle.

Front

What is the radius of the circle given by the equation (x - 2)² + (y + 5)² = 36?

Back

The radius is 6.

Front

How can you identify the radius from the equation of a circle in standard form?

Back

The radius can be identified as the square root of the value on the right side of the equation in standard form.

Front

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

Back

The equation is x² + y² = 25.

Front

What does it mean if the radius of a circle is zero?

Back

If the radius of a circle is zero, it means the circle is a single point located at the center.