Circle Equations and Properties

This video tutorial covers writing equations of circles, including identifying the center and radius. It provides examples of solving circle equations and introduces the concept of completing the square, which is applied to circle equations. The tutorial also explains how to convert equations to standard form and solve quadratic equations using completing the square.

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

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

Tags

CCSS.HSG.GPE.A.1

If the center of a circle is at (-1, 2) and the radius is 14, what is the equation of the circle?

• (x - 1)^2 + (y + 2)^2 = 196

• (x + 1)^2 + (y + 2)^2 = 14

• (x - 1)^2 + (y - 2)^2 = 14

• (x + 1)^2 + (y - 2)^2 = 196

Tags

CCSS.HSG.GPE.A.1

How do you determine the center of a circle when given two intersecting diameters?

• The center is at the midpoint of the radius.

• The center is at the endpoint of one diameter.

• The center is at the intersection of the diameters.

• The center is at the midpoint of one diameter.

Tags

CCSS.7.G.B.4

Given the area of a circle as 16π, what is the radius?

• 2

• 4

• 8

• 16

Tags

CCSS.7.G.B.4

What is the formula for the circumference of a circle?

• 2πr

• 2πd

• πr^2

• πd

Tags

CCSS.HSA-REI.B.4B

What is the purpose of completing the square in algebra?

• To solve linear equations

• To convert quadratic equations into a form that can be easily solved

• To factor polynomials

• To simplify fractions

Tags

CCSS.HSA-REI.B.4B

In completing the square, what value is added to both sides of the equation?

• b/2

• b^2

• (b/2)^2

• 2b

Tags

CCSS.HSA-REI.B.4B

What is the result of completing the square for x^2 - 8x?

• (x + 8)^2

• (x + 4)^2

• (x - 4)^2

• (x - 8)^2

Tags

CCSS.HSG.GPE.A.1

How do you find the center of a circle from its equation in standard form?

• The constants added to x and y

• The square root of the radius

• The coefficients of x and y

• The opposite of the constants in the equation

Tags

CCSS.HSG.GPE.A.1

What is the radius of a circle if its equation is (x - 6)^2 + (y - 1)^2 = 49?

• 6

• 7

• 8

• 49

Tags

CCSS.HSG.GPE.A.1