Question 1: Write the equation of a circle with radius 5 centered at the origin.

Answer: x^2 + y^2 = 25

Question 2: Determine the radius of the circle given by the equation x^2 + y^2 = 81.

Answer: 9

Question 3: Plot the graph of y = 3x on the grid. Describe the circle formed if the equation is x^2 + y^2 = r^2.

Answer: Circle with radius r, where r^2 is determined by context or additional info.

Question 4: Construct a circle with radius 7 centered at the origin on the grid. Write its equation.

Answer: x^2 + y^2 = 49

Question 5: If a circle has the equation x^2 + y^2 = 36, what is its diameter?

Answer: 12

Question 6: A circle passes through the point (4, 3). Find the radius of the circle centered at the origin.

Answer: 5

Question 7: What is the equation of a circle with radius 8 centered at the origin?

Answer: x^2 + y^2 = 64

Question 8: Solve for r if the equation x^2 + y^2 = r^2 is given, and the circle passes through (6, 8).

Answer: r = 10

Question 9: Identify the common feature of all circles centered at the origin based on their equations.

Answer: They all have the form x^2 + y^2 = r^2.

Question 10: A circle has the equation x^2 + y^2 = 100. What is the area enclosed by this circle?

Answer: approximately 314.16

Question 11: Identify and correct the mistake: The equation of a circle centered at the origin with radius 4 is y^2 + x^2 = 16.

Answer: No mistake; the equation is correct.

Question 12: A circle with radius 6 is centered at the origin. Write its equation and determine the length of the radius on the coordinate plane.

Answer: Equation: x^2 + y^2 = 36; radius length is 6 units.