Circle Equations and Properties

Mr. Kenan Ola explains how to graph a circle given its equation. The video covers the formula derivation using the Pythagorean theorem, identifying the center and radius, and provides three examples of graphing circles. Each example demonstrates how to manipulate the equation to find the center and radius, and how to use a compass to draw the circle accurately.

What is the primary mathematical theorem used to derive the formula for a circle?

• Binomial theorem

• Euclidean algorithm

• Fundamental theorem of calculus

• Pythagorean theorem

In the circle formula, what do the variables H and K represent?

• The diameter

• The center of the circle

• The radius

• The circumference

What is the significance of the negative sign in the circle's formula (x - h)^2 + (y - k)^2 = r^2?

• It indicates the circle's diameter

• It shows the circle's circumference

• It helps determine the center's coordinates

• It is used to calculate the area

If the equation of a circle is (x + 2)^2 + (y - 1)^2 = 9, what is the center of the circle?

• (2, 1)

• (-2, -1)

• (-2, 1)

• (2, -1)

If a circle's equation is (x + 2)^2 + (y - 1)^2 = 9, what is the radius?

• 3

• 2

• 4

• 1

In the first example, what is the y-coordinate of the center for the equation (x + 2)^2 + (y - 1)^2 = 9?

• -2

• 2

• -1

• 1

What is the x-coordinate of the center for the equation (x + 2)^2 + (y - 1)^2 = 9?

• 2

• 1

• -1

• -2

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

• 3

• 4

• 2

• 1

In the first example, what is the x-coordinate of the center for the equation (x + 2)^2 + (y - 1)^2 = 9?

• 2

• -2

• 1

• -1

For the equation (x + 2)^2 + (y - 1)^2 = 9, what is the radius?

• 3

• 4

• 2

• 1