Understanding the Equation of a Circle

This video tutorial explains the equation of a circle, starting with circles centered at the origin and then moving to those not centered at the origin. It highlights that the equation is x² + y² = radius² for circles at the origin and adjusts for circles with different centers by incorporating the center's coordinates into the equation. The video includes practice questions and concludes with a brief mention of future content on tangents.

What is the general form of the equation for a circle centered at the origin?

• x + y = r^2

• x^2 + y^2 = r^2

• x^2 - y^2 = r^2

• x^2 + y^2 = r

If a circle has a radius of 7, what is the equation of the circle centered at the origin?

• x^2 + y^2 = 14

• x^2 + y^2 = 21

• x^2 + y^2 = 7

• x^2 + y^2 = 49

How does the equation of a circle change when its center is moved from the origin?

• The radius is squared

• The coordinates of the center are added to x and y

• The coordinates of the center are subtracted from x and y

• The equation remains the same

For a circle with center (2, -3), what is the correct form of the equation?

• (x - 2)^2 + (y - 3)^2 = r^2

• (x - 2)^2 + (y + 3)^2 = r^2

• (x + 2)^2 + (y - 3)^2 = r^2

• (x + 2)^2 + (y + 3)^2 = r^2

What should you remember to do with the signs of the center coordinates in the circle's equation?

• Keep them the same

• Change them

• Double them

• Ignore them

What is the first step in finding the equation of a circle?

• Identify the radius

• Identify the center point

• Square the radius

• Add the center coordinates

What is needed to write the equation of a circle?

• Only the radius

• Neither the center point nor the radius

• Only the center point

• Both the center point and the radius

What is the equation of a circle with center (-4, 5) and radius 3?

• (x - 4)^2 + (y - 5)^2 = 9

• (x + 4)^2 + (y + 5)^2 = 9

• (x - 4)^2 + (y + 5)^2 = 9

• (x + 4)^2 + (y - 5)^2 = 9

What will be covered in the next video?

• How to find the radius of a circle

• How to find the center of a circle

• How to find the equation of a tangent to a circle

• How to graph a circle