Circle Geometry Concepts

Dr. Roger explains a SAT problem involving the equation of a circle. He starts by introducing the general equation of a circle and then demonstrates how to find the center and radius using given points on the diameter. The center is calculated as the midpoint of the diameter, and the radius is half the diameter's length. The video concludes with a reminder to memorize the circle equation and apply these methods to solve similar SAT questions.

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

• x^2 + y^2 = r^2

• x - h + y - k = r

• x - h^2 + y - k^2 = r^2

• x - h^2 + y - k^2 = r

In the equation of a circle, what do the variables h and k represent?

• The center of the circle

• The radius of the circle

• The endpoints of the diameter

• The circumference of the circle

How do you find the x-coordinate of the center of a circle given the endpoints of its diameter?

• Multiply the x-coordinates of the endpoints

• Add the x-coordinates of the endpoints

• Subtract the x-coordinates of the endpoints

• Find the average of the x-coordinates of the endpoints

What is the y-coordinate of the center if the endpoints of the diameter are (-3, 10) and (3, 10)?

• 10

• 3

• 0

• 5

What is the equation of the circle if the center is at (0, 10)?

• (x - 0)^2 + (y - 10)^2 = r^2

• (x - 10)^2 + y^2 = r^2

• (x - 10)^2 + (y - 0)^2 = r^2

• x^2 + (y - 10)^2 = r^2

Which choice is the only possible correct answer if the equation has x^2?

• Choice D

• Choice C

• Choice B

• Choice A

What is the formula to calculate the distance between two points?

• sqrt((x2 + x1)^2 + (y2 + y1)^2)

• x2 - x1 - y2 - y1

• x2 - x1 + y2 - y1

• sqrt((x2 - x1)^2 + (y2 - y1)^2)

What is the length of the diameter if the endpoints are (-3, 10) and (3, 10)?

• 12

• 3

• 6

• 9

How do you find the radius from the diameter?

• Subtract 2 from the diameter

• Add 2 to the diameter

• Divide the diameter by 2

• Multiply the diameter by 2

What is the value of r^2 if the radius is 3?

• 9

• 12

• 6

• 3