Writing Equations of Circles in Center-Radius Form

This video tutorial by Mr. Wit from Fort B Tutoring covers the center-radius form of circles. It begins with an introduction to the concept and proceeds to solve various problems, including finding the center and radius from given equations, using the distance formula and Pythagorean theorem, and determining the center from the midpoint of a diameter. The tutorial also explores using tangent lines and the area of a circle to find the radius. The video concludes with solving a system of equations to determine the center and radius of a circle.

Given a center at (3, -2) and a radius of 5, what is the center-radius form of the circle?

• (x - 5)^2 + (y + 5)^2 = 10

• (x + 3)^2 + (y + 2)^2 = 5

• (x + 3)^2 + (y - 2)^2 = 25

• (x - 3)^2 + (y + 2)^2 = 25

How do you find the radius from the equation x^2 + y^2 = 225?

• Radius = 5

• Radius = 45

• Radius = 225

• Radius = 15

If a circle's equation is x^2 + (y + 2)^2 = 236, what is the y-coordinate of its center?

• 236

• -2

• 2

• 0

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

• (4, 0)

• (-4, 0)

• (0, 4)

• (9, 9)

What represents the center of a circle in the center-radius form?

• (h, k)

• (x, y)

• (r, r)

• (0, 0)

What is the radius of a circle if its area is 25π?

• 50

• π

• 5

• 25

How do you find the center of a circle given the endpoints of its diameter at (-5, 6) and (1, -2)?

• (-2, 2)

• (3, 2)

• (2, -2)

• (-3, -4)

For a circle tangent to x=2, x=8, and y=3, where is the center located?

• (8, 3)

• (2, 3)

• (3, 2)

• (5, 6)

Given three points on a circle, (-4, -3), (-2, 1), and (5, -6), what is the radius?

• 5

• √29

• 10

• 25

What is the center-radius form equation for a circle with a center at (1, -3) and a radius of 5?

• (x + 1)^2 + (y + 3)^2 = 5

• (x - 5)^2 + (y + 5)^2 = 10

• (x + 1)^2 + (y - 3)^2 = 25

• (x - 1)^2 + (y + 3)^2 = 25