Equation of a Circle

Front

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

Back

(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

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

Back

The center is the midpoint of the endpoints. Use the formula: ((x1 + x2)/2, (y1 + y2)/2).

Tags

CCSS.HSG.GPE.B.6

Front

What is the radius of a circle if the equation is given as (x - 3)² + (y + 2)² = 16?

Back

The radius is √16 = 4.

Tags

CCSS.HSG.GPE.A.1

Front

What does the equation x² + y² = r² represent?

Back

It represents a circle centered at the origin (0, 0) with radius r.

Tags

CCSS.HSG.GPE.A.1

Front

If a circle has a center at (2, -3) and a radius of 5, what is its equation?

Back

(x - 2)² + (y + 3)² = 25.

Tags

CCSS.HSG.GPE.A.1

Front

What is the distance formula used to find the distance between two points (x1, y1) and (x2, y2)?

Back

d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

Complete the square for both x and y terms.

Tags

CCSS.HSG.GPE.A.1

Front

What is the center of the circle described by the equation x² + y² - 4x + 6y + 9 = 0?

Back

The center is (2, -3).

Tags

CCSS.HSG.GPE.A.1

Front

What is the radius of the circle with the equation (x + 1)² + (y - 4)² = 36?

Back

The radius is √36 = 6.

Tags

CCSS.HSG.GPE.A.1

Front

What is the significance of the term 'h' in the equation of a circle?

Back

The term 'h' represents the x-coordinate of the center of the circle.

Tags

CCSS.HSG.GPE.A.1