Understanding the Equation of a Circle

The video tutorial explains how to determine the equation of a circle in standard form. It begins by identifying the center of the circle from a graph and then calculates the radius using the distance formula. The tutorial simplifies the radius calculation and concludes by writing the final equation of the circle in standard form.

What is the standard form of the equation of a circle?

• x^2 + y^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

• x^2 - y^2 = r^2

If the center of a circle is at (2, -3), what are the values of h and k?

• h = -2, k = -3

• h = -2, k = 3

• h = 2, k = 3

• h = 2, k = -3

Which formula is used to calculate the distance between two points?

• Quadratic formula

• Midpoint formula

• Slope formula

• Distance formula

What is the distance between the points (2, -3) and (8, 3)?

• Square root of 72

• 12

• 6

• Square root of 36

How do you simplify the square root of 72?

• 12

• 6√2

• 6

• 8√3

What is the value of r squared if r is the square root of 72?

• 36

• 18

• 72

• 144

What is the simplified form of the radius if r equals the square root of 72?

• 12

• 6√2

• 6

• 8√3

In the equation (x - 2)^2 + (y + 3)^2 = 72, what is the center of the circle?

• (2, 3)

• (-2, 3)

• (-2, -3)

• (2, -3)

What is the final form of the equation of the circle with center (2, -3) and radius √72?

• (x + 2)^2 + (y + 3)^2 = 72

• (x + 2)^2 + (y - 3)^2 = 72

• (x - 2)^2 + (y + 3)^2 = 72

• (x - 2)^2 + (y - 3)^2 = 72

What does the term (y + 3) in the equation (x - 2)^2 + (y + 3)^2 = 72 represent?

• The x-coordinate of the center

• The y-coordinate of the center

• The radius

• The diameter