The Basics of Circles (area/circumference, standard/gen form)

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.

Tags

CCSS.HSG.GPE.A.1

Front

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

Back

The general form of the equation of a circle is x² + y² + Dx + Ey + F = 0, where D, E, and F are constants.

Tags

CCSS.HSG.GPE.A.1

Front

How do you find the area of a circle?

Back

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

Tags

CCSS.7.G.B.4

Front

How do you find the circumference of a circle?

Back

The circumference C of a circle is calculated using the formula C = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the radius of a circle?

Back

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

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius, or the distance across the circle through its center.

Tags

CCSS.HSG.C.A.2

Front

How do you convert the standard form of a circle to general form?

Back

To convert (x - h)² + (y - k)² = r² to general form, expand and rearrange to the form x² + y² + Dx + Ey + F = 0.

Tags

CCSS.HSG.GPE.A.1

Front

What is the center of a circle?

Back

The center of a circle is the point (h, k) in the standard form equation (x - h)² + (y - k)² = r².

Tags

CCSS.HSG.GPE.A.1

Front

What is a sector of a circle?

Back

A sector of a circle is a region bounded by two radii and the arc between them.

Front

How do you find the area of a sector?

Back

The area of a sector is calculated using the formula A = (θ/360) * πr², where θ is the angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5