Understanding Circles: Center and Radius

This video tutorial explains how to determine the center and radius of a circle using its equation. It begins with a review of the standard circle equation and demonstrates how to find the center and radius from a given equation. The tutorial also covers how to write the equation of a circle when given the endpoints of its diameter, using the midpoint formula to find the center and calculating the radius. Key concepts include understanding the circle equation, calculating the center and radius, and applying the midpoint formula.

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

• X squared plus Y squared equals R

• X squared plus Y squared equals R squared

• X minus H squared plus Y minus K squared equals R squared

• X plus H squared plus Y plus K squared equals R

In the equation (X - 4)^2 + (Y + 1)^2 = 9, what is the center of the circle?

• (4, 1)

• (-4, -1)

• (4, -1)

• (-4, 1)

What is the radius of the circle given by the equation (X - 4)^2 + (Y + 1)^2 = 9?

• 1

• 4

• 9

• 3

How does translating a circle affect its equation?

• It changes both the center and radius

• It does not affect the equation

• It changes the center

• It changes the radius

If a circle is translated 4 units right and 1 unit down, what is the new center if the original center was at the origin?

• (4, -1)

• (-4, -1)

• (4, 1)

• (-4, 1)

What is the midpoint formula used to find the center of a circle from its diameter?

• ((X1 - X2)/2, (Y1 - Y2)/2)

• (X1 - X2, Y1 - Y2)

• ((X1 + X2)/2, (Y1 + Y2)/2)

• (X1 + X2, Y1 + Y2)

Given the endpoints of a diameter (-2, 5) and (-2, -3), what is the center of the circle?

• (-2, 4)

• (-2, 0)

• (-2, 1)

• (-2, -1)

How do you calculate the radius if the diameter is known?

• Multiply the diameter by 2

• Subtract 2 from the diameter

• Divide the diameter by 2

• Add 2 to the diameter

What is the radius of a circle if its diameter is 8?

• 8

• 2

• 4

• 16

What is the equation of a circle with center (-2, 1) and radius 4?

• (X + 2)^2 + (Y - 1)^2 = 16

• (X - 2)^2 + (Y + 1)^2 = 16

• (X + 2)^2 + (Y + 1)^2 = 16

• (X - 2)^2 + (Y - 1)^2 = 16