Circle Equations and Properties

This video tutorial covers the equations of circles, starting with the basic form where the center is at the origin and then moving to cases where the center is not at the origin. It explains how to find the radius when a point on the circle is given and demonstrates reverse engineering to find the center and radius from a given circle equation.

What is the equation of a circle with its center at the origin and a radius of 5?

• x^2 + y^2 = 25

• x^2 + y^2 = 5

• x + y = 25

• x^2 + y^2 = 10

If the center of a circle is at (0, 0) and the radius is 7, what is the equation of the circle?

• x^2 + y^2 = 7

• x^2 + y^2 = 49

• x^2 + y^2 = 14

• x + y = 49

If the center of a circle is at (-5, 4) and the radius is sqrt(15), what is the equation of the circle?

• (x + 5)^2 + (y - 4)^2 = 15

• (x - 5)^2 + (y + 4)^2 = 15

• (x + 5)^2 + (y - 4)^2 = 225

• (x - 5)^2 + (y + 4)^2 = 225

What is the equation of a circle with center at (3, -2) and radius 4?

• (x + 3)^2 + (y - 2)^2 = 4

• (x - 3)^2 + (y + 2)^2 = 4

• (x + 3)^2 + (y - 2)^2 = 16

• (x - 3)^2 + (y + 2)^2 = 16

If the center of a circle is at (1, -1) and the radius is 3, what is the equation of the circle?

• (x + 1)^2 + (y - 1)^2 = 9

• (x - 1)^2 + (y + 1)^2 = 9

• (x + 1)^2 + (y - 1)^2 = 3

• (x - 1)^2 + (y + 1)^2 = 3

What is the value of the radius if the center is at (-2, 4) and the circle passes through the point (-6, 7)?

• 6

• 3

• 4

• 5

Given the equation (x + 2)^2 + (y - 4)^2 = 25, what is the center of the circle?

• (-2, 4)

• (2, -4)

• (4, -2)

• (-4, 2)

What is the radius of the circle with the equation (x + 2)^2 + (y - 4)^2 = 25?

• 5

• 4

• 3

• 6

What is the radius of a circle with the equation (x - 4)^2 + (y + 1)^2 = 9?

• 3

• 5

• 4

• 2

Given the equation (x - 3)^2 + (y + 2)^2 = 16, what is the center of the circle?

• (3, -2)

• (-3, 2)

• (2, -3)

• (-2, 3)