Understanding the Equation of a Circle

This video tutorial explains how to transform a given circle equation into its standard form. It covers the process of completing the square to form perfect square trinomials, factoring the equation, and determining the circle's center and radius. Finally, it demonstrates how to graph the circle using the center and radius.

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

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 + 2hx + 2ky = r^2

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 = r^2

Why do we need perfect square trinomials in the equation of a circle?

• To simplify the equation

• To find the center and radius

• To ensure the equation is quadratic

• To make the equation linear

What is the first step in simplifying the given circle equation?

• Multiply both sides by two

• Add a constant to both sides

• Divide both sides by two

• Subtract a constant from both sides

After dividing by two, what should be the coefficients of x^2 and y^2?

• Two

• One

• Zero

• Negative one

How do you create a perfect square trinomial from a quadratic expression?

• Subtract the square of half the linear coefficient

• Subtract the square of the constant term

• Add the square of half the linear coefficient

• Add the square of the constant term

What constant is added to both sides to complete the square for x in the equation?

• 8

• 12

• 16

• 4

What is the result of factoring the trinomial x^2 + 8x + 16?

• (x + 8)(x + 2)

• (x - 4)(x - 4)

• (x + 4)(x + 4)

• (x - 8)(x - 2)

What is the center of the circle given by the equation (x + 4)^2 + (y - 3)^2 = 16?

• (4, 3)

• (-4, -3)

• (-4, 3)

• (4, -3)

What is the radius of the circle with the equation (x + 4)^2 + (y - 3)^2 = 16?

• 2

• 4

• 3

• 5

How do you graph a circle with center (-4, 3) and radius 4?

• Plot the center and draw a rectangle

• Plot the center and draw a circle with radius 4

• Plot the center and draw a triangle

• Plot the center and draw a square