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

Answer: x^2 + y^2 = 25

Question 2: Calculate the radius of a circle with the equation x^2 + y^2 = 49.

Answer: 7

Question 3: Given the circle equation x^2 + y^2 = 144, find the diameter.

Answer: 24

Question 4: Plot the graph of the circle with equation x^2 + y^2 = 36 on the grid provided.

Answer: Center at (0,0), radius = 6

Question 5: Construct a circle with radius 4 on the grid centered at the origin. Write its equation.

Answer: x^2 + y^2 = 16

Question 6: Explain why the equation x^2 + y^2 = r^2 represents a circle centered at the origin.

Answer: Because the equation has no xy term and the center is at (0,0), the radius r determines the size of the circle.

Question 7: If a circle has equation x^2 + y^2 = 81, what is its radius? Show your working.

Answer: 9

Question 8: A circle passes through the point (3,4). Find the radius of the circle with center at the origin.

Answer: 5

Question 9: A student mistakenly writes the equation x^2 + y^2 = -25 for a circle. Identify the error and explain why it cannot be a circle.

Answer: The radius squared cannot be negative; thus, no real circle exists with that equation.

Question 10: Challenge: Derive the general form of a circle equation centered at the origin and explain each term.

Answer: The general form is x^2 + y^2 = r^2, where x^2 and y^2 are the squares of the coordinates, and r^2 is the radius squared, representing the distance from the center at (0,0).