Equation of the Circle

Front

What is the standard equation of a circle?

Back

The standard equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

What do the variables (h, k) represent in the circle equation?

Back

The variables (h, k) represent the coordinates of the center of the circle.

Front

How do you find the radius from the circle equation (x - h)² + (y - k)² = r²?

Back

The radius r is the square root of the value on the right side of the equation.

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius.

Front

If the radius of a circle is 5 units, what is the diameter?

Back

The diameter is 10 units.

Front

What are the coordinates of the center of the circle in the equation (x - 4)² + (y - 3)² = 25?

Back

The center is at (4, 3).

Front

How do you determine the center of a circle given its diameter endpoints?

Back

The center is the midpoint of the endpoints of the diameter.

Front

What is the midpoint formula for finding the center of a circle?

Back

The midpoint M between two points (x1, y1) and (x2, y2) is M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the radius of a circle with the equation (x - 2)² + (y + 1)² = 16?

Back

The radius is 4 units, since r² = 16.

Front

What does the equation x² + y² = 9 represent?

Back

It represents a circle centered at the origin (0, 0) with a radius of 3 units.