Exploring Adding and Subtracting Rational Expressions

This video tutorial covers the standard form equation of a circle, explaining how to identify the center and radius. It demonstrates graphing circles and converting equations from general to standard form using the method of completing the square. The tutorial also includes practical examples to illustrate these concepts.

What does the 'HK' in the standard form equation of a circle represent?

• The circle's circumference

• The circle's center

• The circle's radius

• The circle's diameter

Tags

CCSS.HSG.GPE.A.1

How is the radius of a circle determined from its standard form equation?

• By doubling the HK values

• By squaring the coefficient of x

• By taking the square root of the constant term

• By halving the constant term

Tags

CCSS.7.G.B.4

What is the diameter of a circle if its radius is 6.5?

• 6.5

• 13

• 19.5

• 3.25

Tags

CCSS.7.G.B.4

How do you calculate the circumference of a circle?

• 2πr

• πd

• πr^2

• 2r

Tags

CCSS.7.G.B.4

What is the area of a circle with a radius squared value of 81?

• 81π

• 162π

• 40.5π

• 9π

Tags

CCSS.HSG.GPE.A.1

What does the general form of a circle's equation look like?

• x^2 + y^2 = r^2

• (x-h)^2 + (y-k)^2 = r^2

• Ax^2 + By^2 = C

• x^2 + y^2 + Cx + Dy + E = 0

Tags

CCSS.HSG.GPE.A.1

What is the purpose of completing the square when converting a circle's equation from general to standard form?

• To identify the circle's center and radius

• To simplify the equation

• To find the circle's diameter

• To calculate the circle's area

Tags

CCSS.HSG.GPE.A.1

What is the center of a circle in the equation (x-1)^2 + (y+3)^2 = 16?

• (1, -3)

• (-1, -3)

• (-1, 3)

• (1, 3)

Tags

CCSS.HSG.GPE.A.1

What is the radius of a circle whose equation is x^2 + y^2 - 14x - 8y + 49 = 0 after completing the square?

• 14

• 4

• 49

• 7

Tags

CCSS.HSG.GPE.A.1

In the process of completing the square for a circle's equation, what do you do with the constant term?

• Square it

• Divide it by 2

• Move it to the other side of the equation

• Multiply it by 2

Tags

CCSS.HSG.GPE.A.1