Equation of a Circle

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 radius from the equation of a circle?

Back

The radius can be found by taking the square root of the number on the right side of the equation in standard form: (x - h)² + (y - k)² = r².

Front

What is the center of the circle in the equation (x - 5)² + (y + 2)² = 36?

Back

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

Front

If the equation of a circle is (x + 1)² + (y - 4)² = 25, what is the radius?

Back

The radius is 5.

Front

Write the equation of a circle with center (0, 0) and radius 4.

Back

The equation is x² + y² = 16.

Front

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

Back

The term (h, k) represents the coordinates of the center of the circle.

Front

In the equation (x - 3)² + (y + 4)² = 121, what is the radius?

Back

The radius is 11.

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

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 (7, 0) and radius 3?

Back

The equation is (x - 7)² + y² = 9.