Circle Equations and Properties

This video tutorial covers the basics of circle equations, focusing on the formula (X - H)^2 + (Y - K)^2 = R^2. It explains how to identify the center (H, K) and radius (R) of a circle from the equation. The tutorial provides examples to illustrate how to plug in values for the center and radius, and discusses the significance of subtraction signs in determining the center's coordinates. The video concludes with a final example, emphasizing the concept of the origin when both H and K are zero.

What is the general formula for a circle in a coordinate plane?

• X squared plus Y squared equals R squared

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

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

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

In the circle equation X minus H squared plus Y minus K squared equals R squared, what do H and K represent?

• The circumference of the circle

• The diameter of the circle

• The coordinates of the center

• The radius of the circle

If a circle has a center at (-4, 6) and a radius of 12, what is the equation of the circle?

• X minus 4 squared plus Y minus 6 squared equals 144

• X plus 4 squared plus Y plus 6 squared equals 144

• X plus 4 squared plus Y minus 6 squared equals 144

• X minus 4 squared plus Y plus 6 squared equals 144

What happens to the center of the circle if the subtraction signs in the equation are changed?

• The center coordinates are halved

• The center coordinates are doubled

• The center coordinates are inverted

• The center remains the same

If the equation of a circle is X minus 8 squared plus Y plus 2 squared equals 121, what is the center of the circle?

• (-8, -2)

• (8, -2)

• (8, 2)

• (-8, 2)

What is the radius of a circle if its equation is X minus 8 squared plus Y plus 2 squared equals 121?

• 12

• 9

• 11

• 10

What is the significance of the subtraction signs in the circle equation X minus H squared plus Y minus K squared equals R squared?

• They determine the circumference

• They determine the diameter

• They determine the center coordinates

• They determine the radius

In the equation X squared plus Y squared equals 81, what is the center of the circle?

• (0, 0)

• (9, 9)

• (1, 1)

• (81, 81)

What is the radius of a circle with the equation X squared plus Y squared equals 81?

• 9

• 81

• 8

• 10

If a circle's equation is X squared plus Y squared equals 81, what can be inferred about its center?

• The center is at (1, 1)

• The center is at (0, 0)

• The center is at (9, 9)

• The center is at (81, 81)