How to find the center and radius of a circle in standard form

The video tutorial explains how to find the center and radius of a circle from its equation. It begins with an introduction to the problem and the standard form of a circle's equation. The instructor then demonstrates the process of completing the square to transform the given equation into standard form. Finally, the video shows how to identify the circle's center and radius from the transformed equation.

What is the first step in solving the problem of finding the center and radius of a circle from its equation?

• Find the slope of the tangent

• Calculate the diameter of the circle

• Determine if the equation is in standard form

• Sketch the graph of the circle

What does the standard form of a circle's equation look like?

• (X - H)^2 + (Y - K)^2 = R^2

• X^2 + Y^2 + 2X + 2Y = R^2

• X^2 + Y^2 + 4X - 10Y = 0

• X^2 + Y^2 = R^2

What is the purpose of completing the square in the context of circle equations?

• To convert the equation into a perfect square trinomial

• To find the slope of the circle

• To determine the diameter of the circle

• To eliminate the constant term

When completing the square, what should you do after adding a number to one side of the equation?

• Divide the equation by the number

• Add the same number to the other side

• Subtract the same number from the other side

• Multiply the equation by the number

What is the center of the circle after completing the square for the given equation?

• (5, -2)

• (-2, 5)

• (2, -5)

• (-5, 2)

What is the radius of the circle after completing the square for the given equation?

• 7

• 6

• 8

• 5

Why is it important to balance the equation when completing the square?

• To maintain the equality of the equation

• To ensure the equation remains a circle

• To simplify the graphing process

• To find the tangent line