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.

Tags

CCSS.HSG.GPE.A.1

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).

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.HSG.C.A.2

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.

Tags

CCSS.HSG.GPE.A.1

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.

Tags

CCSS.7.G.B.4

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.

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The equation is x² + y² = 25.

Tags

CCSS.HSG.GPE.A.1