Circle Equations and Their Forms

This video tutorial explains how to write the equation of a circle in general form. It begins with an introduction to the general form equation and demonstrates how to convert a circle equation from standard form to general form by expanding it. The tutorial provides two examples: the first involves expanding a given equation, and the second involves finding the radius of a circle given its center and a point it passes through, followed by converting the equation to general form.

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

• x^2 + y^2 = r^2

• x^2 + y^2 + Dx + Ey + F = 0

• x^2 + y^2 + 2x + 2y = 0

• (x - h)^2 + (y - k)^2 = r^2

What is the first step in converting a circle's equation from standard form to general form?

• Factor the equation

• Expand the binomials

• Combine like terms

• Find the radius

How do you expand (X + 5)^2?

• X^2 + 10X + 25

• X^2 + 5X + 25

• X^2 + 25

• X^2 + 5X + 5

What is the result of expanding (Y - 3)^2?

• Y^2 - 6Y + 9

• Y^2 - 3Y + 9

• Y^2 - 9

• Y^2 - 6Y

What is the next step after expanding the binomials in the circle's equation?

• Solve for Y

• Combine like terms

• Find the center

• Calculate the radius

What is the final general form equation for the first question?

• x^2 + y^2 + 10x - 6y + 25 = 0

• x^2 + y^2 + 10x - 6y = 18

• x^2 + y^2 + 10x - 6y + 18 = 0

• x^2 + y^2 + 10x - 6y + 16 = 0

What information is given in the second question about the circle?

• The center and a point it passes through

• The diameter and a point it passes through

• The radius and diameter

• The circumference and area

How do you find the radius of the circle in the second question?

• By expanding the equation

• By using the distance formula

• By using the midpoint formula

• By solving for x

What is the radius of the circle in the second question?

• 5

• 3

• 4

• 6

What is the standard form equation of the circle in the second question before converting?

• (X + 1)^2 + (Y + 1)^2 = 5

• (X + 1)^2 + (Y + 1)^2 = 25

• (X - 1)^2 + (Y - 1)^2 = 5

• (X - 1)^2 + (Y - 1)^2 = 25