Understanding Circle Equations in Standard Form

The video tutorial explains how to determine the equation of a circle in standard form. It begins by defining the standard form equation and identifying the components: center (h, k) and radius (r). The first example demonstrates a circle centered at the origin, showing how to calculate the radius from a graph and derive the equation. The second example covers a circle with a center at (-3, 4), again determining the radius and forming the equation. The tutorial emphasizes understanding the relationship between the circle's geometric properties and its algebraic representation.

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

• x^2 + y^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = 2r

• (x + h)^2 + (y + k)^2 = r^2

Tags

CCSS.HSG.GPE.A.1

If a circle is centered at the origin and has a radius of 6, what is its equation?

• (x - 6)^2 + (y - 6)^2 = 36

• x^2 + y^2 = 36

• (x + 6)^2 + (y + 6)^2 = 36

• x^2 + y^2 = 12

How do you determine the radius of a circle from a graph?

• Measure the distance from the center to any point on the circle

• Measure the diameter and divide by two

• Measure the distance between two points on the circle

• Measure the circumference and divide by pi

Tags

CCSS.HSG.GPE.A.1

What are the coordinates of the center of a circle if h = -3 and k = 4?

• (3, -4)

• (-3, 4)

• (-4, 3)

• (4, -3)

Tags

CCSS.HSG.GPE.A.1

For a circle with center (-3, 4) and radius 4, what is the equation in standard form?

• (x - 3)^2 + (y - 4)^2 = 16

• (x - 3)^2 + (y + 4)^2 = 16

• (x + 3)^2 + (y - 4)^2 = 16

• (x + 3)^2 + (y + 4)^2 = 16

Tags

CCSS.HSG.GPE.A.1

What is the simplified form of (x - (-3))^2?

• (x + 4)^2

• (x - 4)^2

• (x - 3)^2

• (x + 3)^2

Tags

CCSS.HSG.GPE.A.1

What is the radius of a circle if its equation is (x + 3)^2 + (y - 4)^2 = 16?

• 2

• 4

• 16

• 8

Tags

CCSS.HSG.GPE.A.1