Circle Equations

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 find 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 is the radius of a circle if the equation is (x + 3)² + (y - 4)² = 25?

Back

The radius is 5, since r² = 25, thus r = √25 = 5.

Front

If the diameter of a circle is 12, what is the radius?

Back

The radius is 6, since the radius is half of the diameter.

Front

What does 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 + (y - k)² = r² to identify the center and radius of the circle.

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 the x and y terms.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² - 2ab + b², which factors to (a - b)².

Front

Given the equation (x - 1)² + (y + 2)² = 9, what is the center and radius?

Back

The center is (1, -2) and the radius is 3.

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 identify the radius from the equation (x + 2)² + (y - 5)² = 36?

Back

The radius is 6, since r² = 36, thus r = √36 = 6.