Circle Equations and Properties

This video tutorial covers the equations of circles, focusing on finding the center and radius, graphing circles, and writing equations in standard form. It includes solving problems with circles at the origin, displaced centers, and using the distance formula. The video also demonstrates completing the square to convert equations to standard form. Additional resources and practice problems are provided for further learning.

What is the main focus of this video tutorial?

• Exploring trigonometric identities

• Learning about linear functions

• Understanding and graphing circles

• Solving quadratic equations

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

• x^2 - y^2 = r^2

• x + y = r^2

• x^2 + y^2 = r^2

• x^2 + y^2 = r

If a circle's equation is x^2 + y^2 = 9, what is the radius?

• 9

• 3

• 1.5

• 6

How do you determine the center of a circle from the equation (x - h)^2 + (y - k)^2 = r^2?

• The center is (0, 0)

• The center is (h, k)

• The center is (-h, -k)

• The center is (r, r)

In the equation (x - 2)^2 + (y + 1)^2 = 16, what is the center of the circle?

• (-2, -1)

• (2, -1)

• (2, 1)

• (-2, 1)

What is the radius of a circle with the equation (x - 2)^2 + (y + 1)^2 = 16?

• 8

• 2

• 16

• 4

How do you write the equation of a circle with center (-10, 9) and radius 6?

• (x - 10)^2 + (y + 9)^2 = 36

• (x + 10)^2 + (y - 9)^2 = 36

• (x - 10)^2 + (y - 9)^2 = 6

• (x + 10)^2 + (y + 9)^2 = 6

What formula is used to find the radius when given a center and a point on the circle?

• Distance formula

• Pythagorean theorem

• Quadratic formula

• Slope formula

If a circle has a center at (2, -5) and passes through (-7, -1), what is the radius squared?

• 97

• 49

• 81

• 16

What is the first step in converting a circle's equation to standard form using completing the square?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 16 from both sides

• Add 16 to both sides