Circle Geometry Concepts

The video tutorial covers how to write the equation of a circle using its center and radius. It explains transformations of circles and how these affect their equations. Several examples are provided, including a challenge problem that uses the midpoint and distance formulas to find the center and radius of a circle. The Pythagorean theorem is also applied to determine the radius length.

What is the equation of a circle with center at (-11, -8) and radius 4?

• (x - 11)^2 + (y + 8)^2 = 16

• (x - 11)^2 + (y - 8)^2 = 16

• (x + 11)^2 + (y + 8)^2 = 16

• (x + 11)^2 + (y - 8)^2 = 16

If a circle's center is at (16, 6) and it is moved 4 units left and 2 units up, what is the new center?

• (20, 8)

• (20, 4)

• (12, 8)

• (12, 4)

How does moving a circle affect its radius?

• The radius increases

• The radius decreases

• The radius remains the same

• The radius becomes zero

What is the equation of a circle with center at (0, 3) and radius 3?

• x^2 + (y - 3)^2 = 9

• (x - 3)^2 + y^2 = 9

• (x + 3)^2 + y^2 = 9

• x^2 + (y + 3)^2 = 9

What is the term for a line that touches a circle at exactly one point?

• Chord

• Tangent line

• Diameter

• Secant line

How do you find the center of a circle given two endpoints of its diameter?

• Use the slope formula

• Use the Pythagorean theorem

• Use the midpoint formula

• Use the distance formula

What is the radius of a circle if the diameter's endpoints are (-17, -9) and (-19, -9)?

• 3

• 4

• 2

• 1

Which formula can be used to find the length of a radius when given a center and a point on the circle?

• Quadratic formula

• Pythagorean theorem

• Slope formula

• Midpoint formula

If a circle's center is at (1, 1) and a point on the circle is (2, 3), what is the radius?

• 2

• 1

• 3

• √5

What is the equation of a circle with center at (1, 1) and radius √5?

• (x - 1)^2 + (y - 1)^2 = 5

• (x + 1)^2 + (y + 1)^2 = 5

• (x - 1)^2 + (y + 1)^2 = 5

• (x + 1)^2 + (y - 1)^2 = 5