Understanding the Equation of a Circle in Standard Form

The video tutorial explains how to write the equation of a circle in standard form. It begins by introducing the standard form and identifying the center of the circle using coordinates H and K. The tutorial then demonstrates how to calculate the radius of the circle. Finally, it shows how to formulate the circle's equation using the identified center and radius, resulting in the equation (X + 3)^2 + (Y - 4)^2 = 25.

What are the coordinates of the center of a circle in standard form?

• (M, N)

• (A, B)

• (X, Y)

• (H, K)

If the X-coordinate of the center is -3, what is the value of H?

• -4

• 4

• -3

• 3

How do you determine the radius of a circle?

• By measuring the diameter and dividing by 2

• By measuring the area and taking the square root

• By measuring the distance from the center to any point on the circumference

• By measuring the circumference and dividing by π

What is the radius of a circle if the distance from the center to the circumference is 5 units?

• 10

• 25

• 2.5

• 5

What is the standard form equation of a circle with center (-3, 4) and radius 5?

• (X + 3)^2 + (Y - 4)^2 = 25

• (X - 3)^2 + (Y + 4)^2 = 25

• (X - 3)^2 + (Y - 4)^2 = 25

• (X + 3)^2 + (Y + 4)^2 = 25