10.7 Circle Equations Practice

Front

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

Back

The standard form of a circle's equation is (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 of a circle from its equation?

Back

To find the radius, identify the equation in the form (x - h)² + (y - k)² = r². The radius is the square root of the number on the right side of the equation.

Front

What are the coordinates of the center of a circle given by the equation (x - 5)² + (y + 2)² = 36?

Back

The center of the circle is at (5, -2).

Front

If the radius of a circle is 4, what is the equation of the circle centered at (0, 0)?

Back

The equation is x² + y² = 16.

Front

What is the radius of the circle with the equation (x + 1)² + (y - 3)² = 25?

Back

The radius is 5.

Front

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

Back

To convert, complete the square for the x and y terms in the equation Ax² + Ay² + Bx + Cy + D = 0.

Front

What is the center and radius of the circle given by the equation (x - 2)² + (y + 4)² = 9?

Back

Center: (2, -4), Radius: 3.

Front

Write the equation of a circle with center (3, -1) and radius 2.

Back

The equation is (x - 3)² + (y + 1)² = 4.

Front

What is the radius of the circle defined by the equation x² + y² = 25?

Back

The radius is 5.

Front

What does the term 'completing the square' mean in the context of circle equations?

Back

Completing the square involves rewriting a quadratic expression in the form (x - h)² to help identify the center and radius of the circle.