Question 1: Calculate the radius of a circle with the equation x² + y² = 25.

Answer: 5

Question 2: For the circle x² + y² = r², if the radius is 7 units, write down the equation of the circle.

Answer: x² + y² = 49

Question 3: Identify the radius of the circle given the equation x² + y² = 64.

Answer: 8

Question 4: Plot the graph of y = 2x on the provided grid. What is the radius of the circle passing through the points (3,4) and (−3,4)?

Answer: 5

Question 5: Construct a circle with a radius of 4 units centered at the origin. Write the equation of this circle.

Answer: x² + y² = 16

Question 6: A circular pond has a radius of 6 meters. Write down its equation in the form x² + y² = r².

Answer: x² + y² = 36

Question 7: A drone flies around a circular field centered at the origin with radius 10 units. Its position at a certain moment is at (6,8). Verify if this point lies on the circle.

Answer: Yes

Question 8: Explain why the point (0, r) lies on the circle x² + y² = r².

Answer: Because substituting (0, r) gives 0² + r² = r², which satisfies the equation.

Question 9: A circle is described by the equation x² + y² = 36. Find the length of the diameter.

Answer: 12

Question 10: A circular track has a radius of 15 meters. Calculate the circumference of the track.

Answer: 94.2

Question 11: Error Analysis: A student claims that the point (0, r) does not lie on the circle x² + y² = r². Is this true? Explain your reasoning.

Answer: No, because (0, r) always satisfies x² + y² = r², as 0² + r² = r², which is true.