Circle Equations and Properties

The video tutorial explains how to derive the equation of a circle given its center and a point on the circle. It starts by identifying the center's coordinates and then calculates the radius using the distance formula derived from the Pythagorean Theorem. The tutorial walks through the process of finding changes in x and y to apply the formula, ultimately deriving the circle's equation in standard form.

What is the color of the point that represents the center of the circle?

• Blue

• Green

• Orangeish-red

• Yellow

What are the coordinates of the center of the circle?

• (1, 1)

• (1, -1)

• (-1, 1)

• (0, 0)

What is the formula used to calculate the radius of the circle?

• Area formula

• Circumference formula

• Distance formula

• Volume formula

What is the change in x when moving from the center to the point on the circle?

• 5

• 6

• 7

• 8

What is the change in y when moving from the center to the point on the circle?

• -7

• -6

• -4

• -5

What is the value of r-squared for the circle?

• 74

• 25

• 49

• 100

What is the equation of the circle in terms of x and y?

• (x + 1)^2 + (y + 1)^2 = 74

• (x + 1)^2 + (y - 1)^2 = 74

• (x - 1)^2 + (y + 1)^2 = 74

• (x - 1)^2 + (y - 1)^2 = 74

What operation is performed on the x-coordinate of the center in the circle equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the final simplified form of the circle equation?

• x^2 + y^2 = 74

• (x + 1)^2 + (y - 1)^2 = 74

• (x - 1)^2 + (y + 1)^2 = 74

• (x + 1)^2 + (y + 1)^2 = 74

What is the significance of the number 74 in the circle equation?

• It is the diameter

• It is the circumference

• It is r-squared

• It is the area