3.1 Writing Equations of 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 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 found at the point (h, k).

Front

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

Back

The radius (r) in the equation (x - h)² + (y - k)² = r² represents the distance from the center of the circle to any point on its circumference.

Front

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

Back

The radius is 3, since r² = 9, therefore r = √9 = 3.

Front

What is the center of the circle in the equation (y - 5)² + (x + 3)² = 16?

Back

The center is at (-3, 5).

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

Back

The equation is x² + y² = 25.

Front

In the equation (x + 4)² + (y - 1)² = 36, what is the radius?

Back

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

Front

What does the term (x - h)² represent in the circle's equation?

Back

The term (x - h)² represents the horizontal distance from the center of the circle to a point on the circle.

Front

If the equation of a circle is (x - 2)² + (y + 3)² = 25, what is the center?

Back

The center is at (2, -3).