Master how to determine the center and radius given the equation of a circle

The video tutorial explains how to determine the center and radius of a circle using its equation. It covers the general form of a circle's equation and provides examples to illustrate different scenarios, such as when the center is at the origin, when the radius is not a perfect square, and when coefficients are present in the equation. The tutorial also demonstrates how to simplify square roots when calculating the radius.

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

• X^2 + Y^2 = R^2

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 = H^2 + K^2

• (X + H)^2 + (Y + K)^2 = R^2

If the equation of a circle is X^2 + Y^2 = 9, what is the radius?

• 3

• 9

• 0

• 4.5

How do you find the center of a circle from the equation X^2 + Y^2 = 10?

• (5, 5)

• (0, 0)

• (1, 1)

• (10, 10)

In the equation 2 * (X - 3)^2 + 2 * (Y + 1)^2 = 32, what is the center of the circle?

• (3, 1)

• (-3, -1)

• (-3, 1)

• (3, -1)

What is the radius of the circle given by the equation 2 * (X - 3)^2 + 2 * (Y + 1)^2 = 32?

• 2

• 4

• 8

• 16

How can you express the radius when R^2 = 60?

• 4 * sqrt(15)

• 2 * sqrt(15)

• sqrt(30)

• sqrt(60)

Which of the following is a correct simplification of sqrt(60)?

• 2 * sqrt(15)

• 5 * sqrt(12)

• 4 * sqrt(5)

• 3 * sqrt(10)