How to write the equation of a circle when center is at the origin and radius is given

The video tutorial explains how to derive the equation of a circle. It starts with the general equation for a circle with a center at any point (H, K) and then simplifies it for a circle centered at the origin (0, 0). The instructor demonstrates how to substitute the center coordinates and radius into the equation, resulting in the final form: X^2 + Y^2 = 36, where the radius is 6.

What is the radius of the circle discussed in the video?

• 6

• 7

• 5

• 4

What is the general form of a circle's equation?

• X^2 + Y^2 = R^2

• (X - H)^2 + (Y - K)^2 = R^2

• X + Y = R

• (X + H)^2 + (Y + K)^2 = R^2

When the center of a circle is at the origin, what are the coordinates of the center?

• (1,1)

• (X,Y)

• (0,0)

• (H,K)

How do you modify the circle equation when the center is at the origin?

• Replace R with 0

• Replace X and Y with 0

• Replace H and K with 0

• Replace H and K with 1

What is the final equation of the circle with a radius of 6 and center at the origin?

• X^2 + Y^2 = 12

• X^2 + Y^2 = 36

• X^2 + Y^2 = 6

• X^2 + Y^2 = 18