Circle Equations by Completing the Square

Front

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

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 center of a circle from its equation?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What does the variable 'r' represent in the circle equation?

Back

The variable 'r' represents the radius of the circle.

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x + p)² = q.

Front

How do you complete the square for x² + 14x?

Back

Add (14/2)² = 49 to both sides to get (x + 7)² = 49.

Front

What is the radius of the circle in the equation (x-3)² + (y-2)² = 16?

Back

The radius is 4, since r² = 16.

Front

What does (h, k) represent in the context of a circle?

Back

(h, k) represents the center of the circle.

Front

How do you convert the equation x² + 6x = 5 into standard form?

Back

Complete the square to get (x + 3)² = 14.

Front

What is the significance of the number 16 in the equation (x-3)² + (y-2)² = 16?

Back

It represents the square of the radius of the circle.

Front

What is the first step in completing the square for a quadratic equation?

Back

Move the constant term to the other side of the equation.