Equation of a circle

Front

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

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 radius from the equation (x + 2)² + (y - 3)² = 4?

Back

The radius is the square root of the right side of the equation. Here, r = √4 = 2.

Front

Write the equation of a circle with center (7, 0) and radius 3.

Back

(x - 7)² + (y - 0)² = 3² or (x - 7)² + y² = 9.

Front

What is the circumference of a circle with radius r?

Back

Circumference = 2πr.

Front

What is the area of a circle with radius r?

Back

Area = πr².

Front

Convert the general equation of a circle x² + y² + 4x - 6y + 9 = 0 to standard form.

Back

Complete the square to get (x + 2)² + (y - 3)² = 4.

Front

What does the term 'diameter' refer to in a circle?

Back

The diameter is twice the radius and is the longest distance across the circle.

Front

If the center of a circle is at the origin, what is the equation?

Back

x² + y² = r².

Front

What is the relationship between the radius and diameter?

Back

Diameter = 2 × Radius.

Front

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

Back

From (x - h)² + (y - k)² = r², the center is (h, k).