Graphing and Writing Equations of Circles

The video tutorial provides an overview of circle equations derived from the Pythagorean theorem. It explains how to graph circles, adjust equations for different centers, and write circle equations from given centers and radii. The tutorial also covers completing the square to find circle centers and radii, emphasizing the relationship between circle geometry and algebraic expressions.

What theorem is the equation of a circle based on?

• Fermat's Last Theorem

• Thales' theorem

• Euler's theorem

• Pythagorean theorem

What does the variable 'R' represent in the context of a circle's equation?

• Radius

• Area

• Diameter

• Circumference

How do you adjust the equation of a circle when its center is not at the origin?

• Multiply the equation by -1

• Shift the x and y values

• Change the radius

• No adjustment needed

What is the radius of a circle with the equation x^2 + y^2 = 25?

• 5

• 25

• 10

• 50

For a circle with the equation (x - 3)^2 + (y + 2)^2 = 49, where is the center located?

• (3, -2)

• (-3, 2)

• (3, 2)

• (-3, -2)

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

• (x + h)^2 + (y + k)^2 = r^2

• x^2 + y^2 + r^2 = 0

• (x - h)^2 + (y - k)^2 = r^2

• x^2 + y^2 = r^2

What does the equation (x + 7)^2 + y^2 = 9 represent?

• A circle with center (7, 0) and radius 3

• A circle with center (7, 0) and radius 9

• A circle with center (-7, 0) and radius 9

• A circle with center (-7, 0) and radius 3

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

• To simplify the equation

• To find the circle's diameter

• To determine the center and radius

• To calculate the area of the circle

Given the equation x^2 + y^2 - 6x + 2y + 4 = 0, what is the center of the circle?

• (3, -1)

• (-3, -1)

• (-3, 1)

• (3, 1)

How do you find the radius from an equation in general form?

• Square root of the constant term on the right side after completing the square

• Square root of the sum of squared coefficients

• Half the coefficient of x

• Square root of the constant term