Understanding the Center-Radius Form of a Circle

This video tutorial explains how to find the center-radius form of a circle's equation. It begins with an introduction to the formula, followed by a true/false example problem involving a circle with a given diameter and center. The video then explores how to determine the correct equation for a circle graph, emphasizing the importance of using the correct signs and squaring the radius.

What is the general form of the center-radius equation of a circle?

• X minus H plus Y minus K equals R

• X squared plus Y squared equals R squared

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

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

If a circle has a diameter of 10 cm and is centered at (3, -6), what is the radius?

• 10 cm

• 6 cm

• 3 cm

• 5 cm

In the center-radius equation, how are the signs of H and K used?

• They are used as they are.

• They are reversed.

• Only H is reversed.

• Only K is reversed.

What is the radius of a circle if its diameter is 10 cm?

• 10 cm

• 5 cm

• 20 cm

• 15 cm

For a circle centered at (4, 2) with a radius of 2, what is the correct equation?

• X minus 2 squared plus Y minus 4 squared equals 4

• X minus 2 squared plus Y minus 4 squared equals 2

• X minus 4 squared plus Y minus 2 squared equals 4

• X minus 4 squared plus Y minus 2 squared equals 2

What is the mistake in the equation X minus 2 squared plus Y minus 4 squared equals 4 for a circle centered at (4, 2)?

• The signs of H and K are incorrect.

• The radius is not squared.

• The values of H and K are swapped.

• The equation is correct.

If a circle is centered at (4, 2) and touches the x-axis at (4, 0), what is the radius?

• 4

• 2

• 0

• 6

What is the correct equation for a circle centered at (4, 2) with a radius of 2?

• X minus 4 squared plus Y minus 2 squared equals 2

• X minus 2 squared plus Y minus 4 squared equals 2

• X minus 4 squared plus Y minus 2 squared equals 4

• X minus 2 squared plus Y minus 4 squared equals 4

How do you determine the radius from the diameter?

• Add 2 to the diameter

• Divide the diameter by 2

• Subtract 2 from the diameter

• Multiply the diameter by 2

What is the result of squaring the radius of a circle with a radius of 2?

• 2

• 4

• 16

• 8