Understanding Circle Equations

This video tutorial explains how to write the equation of a circle given different pieces of information. It covers the two main forms of circle equations, demonstrates solving for the equation with a given center and radius, and shows how to find the radius using a point on the circle. Additionally, it explains how to determine the circle's equation using the endpoints of its diameter.

What is the equation of a circle centered at the origin?

• x^2 + y^2 = 2r

• x^2 + y^2 = 2r^2

• x^2 + y^2 = r^2

• x^2 + y^2 = r

When the center of a circle is at (h, k), what is the equation of the circle?

• (x + h)^2 + (y - k)^2 = r^2

• (x - h)^2 + (y + k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

If the radius of a circle is 4, what is r squared?

• 2

• 4

• 8

• 16

What is a common mistake students make when substituting values into the circle equation?

• Using x instead of y

• Using k instead of h

• Using h instead of k

• Using r instead of r squared

How can you find the radius if you have a point on the circle and the center?

• Use the slope formula

• Use the distance formula

• Use the area formula

• Use the midpoint formula

What is the midpoint of the points (3, 2) and (7, -4)?

• (4, 1)

• (5, -1)

• (5, 1)

• (4, -1)

What does the diameter of a circle represent?

• The distance across the circle through the center

• The circumference of the circle

• The area of the circle

• The radius of the circle

If the endpoints of a diameter are given, how can you find the center of the circle?

• Find the slope of the line

• Find the average of the x-coordinates

• Find the midpoint of the endpoints

• Find the average of the y-coordinates

What is the formula for the midpoint of two points (x1, y1) and (x2, y2)?

• ((x1 - x2)/2, (y1 - y2)/2)

• ((x1 / x2)/2, (y1 / y2)/2)

• ((x1 + x2)/2, (y1 + y2)/2)

• ((x1 * x2)/2, (y1 * y2)/2)

What is the final form of the circle equation if the center is (5, -1) and r squared is 13?

• (x + 5)^2 + (y + 1)^2 = 13

• (x - 5)^2 + (y - 1)^2 = 13

• (x + 5)^2 + (y - 1)^2 = 13

• (x - 5)^2 + (y + 1)^2 = 13