Exploring Equations of Circles

This video tutorial covers the equations of circles, explaining the formula and its components, such as the center and radius. It demonstrates how to construct circle equations from given data and graph them. The tutorial includes examples of different circle equations and concludes with a review of key points.

What is the standard form equation of a circle?

• x^2 + y^2 + r^2 = 0

• (x - h)^2 + (y - k)^2 = r^2

• x - h^2 + y - k^2 = r

• x^2 + y^2 = r^2

What do the h and k in the circle equation represent?

• The coordinates of the center

• The slope and y-intercept

• The radius and diameter

• The x and y intercepts

How can the radius of a circle be determined from its equation?

• By adding h and k

• By taking the square root of the right side of the equation

• By squaring the coefficient of x

• By subtracting h from k

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

• 18

• 6

• 9

• 3

Given the equation x^2 + (y - 1)^2 = 1, where is the center of the circle?

• (1, 0)

• (0, -1)

• (-1, 0)

• (0, 1)

How do you graph a circle from its equation?

• Plot the center and draw a line equal to the radius

• Draw a square and inscribe the circle within it

• Plot the center and make a square with sides equal to the diameter

• Plot the center and draw a circle with a compass set to the radius

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

• (x + 2)^2 + (y + 3)^2 = 4

• (x - 2)^2 + (y - 3)^2 = 4

• (x + 2)^2 + (y - 3)^2 = 16

• (x - 2)^2 + (y + 3)^2 = 16

If a circle has a center at (-4, 5) and a radius of 3, what is its equation?

• (x + 4)^2 + (y + 5)^2 = 3

• (x + 4)^2 + (y - 5)^2 = 9

• (x - 4)^2 + (y + 5)^2 = 9

• (x - 4)^2 + (y - 5)^2 = 9

For the equation (x - 1)^2 + (y + 2)^2 = 25, what is the radius of the circle?

• 5

• 50

• 10

• 25

How is the center of the circle determined from the equation (x - 3)^2 + (y + 4)^2 = 36?

• (-3, -4)

• (3, 4)

• (-3, 4)

• (3, -4)