Equation of a Circle

Front

What is the definition of a circle?

Back

A circle is a set of points in a plane that are equidistant from a fixed point called the center.

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

The standard equation is (x - h)² + (y - k)² = r².

Front

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

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

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

Back

The center is (3, 2).

Front

What is the diameter of a circle?

Back

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

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.

Front

What is a tangent line to a circle?

Back

A tangent line is a straight line that touches the circle at exactly one point.

Front

What is the circumference of a circle?

Back

The circumference is the distance around the circle, calculated as C = 2πr.

Front

How do you determine if a point is inside, outside, or on a circle?

Back

Substitute the point's coordinates into the circle's equation and compare the result to r².

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

The equation is x² + y² = 25.