Question 1: Write the equation of a circle with center at (0, 0) and radius 5.

Answer: x^2 + y^2 = 25

Question 2: Calculate the radius of the circle given by the equation x^2 + y^2 = 36.

Answer: 6

Question 3: Determine whether the point (4, 3) lies on the circle x^2 + y^2 = 25. Show your working.

Answer: Yes, because 4^2 + 3^2 = 16 + 9 = 25

Question 4: Plot the graph of the circle x^2 + y^2 = 49 on the grid.

Answer: Student draws circle with radius 7 centered at origin.

Question 5: Construct a circle with radius 8 on the grid. Write its equation.

Answer: x^2 + y^2 = 64

Question 6: A circle has the equation x^2 + y^2 = 81. What is its radius?

Answer: 9

Question 7: Explain why the equation x^2 + y^2 = r^2 always represents a circle centered at the origin.

Answer: Because the general form x^2 + y^2 = r^2 places the center at (0,0), with radius r.

Question 8: A circle passes through the point (6, 8) and has its center at the origin. Find its radius and write the equation.

Answer: radius = 10; equation: x^2 + y^2 = 100

Question 9: Identify and correct the mistake in the equation: x^2 + y^2 = 49, if the circle has its center at (1, 1) and radius 7.

Answer: The correct equation should include the shift: (x - 1)^2 + (y - 1)^2 = 49.

Question 10: Derive the general form of the circle equation with center at (h, k) and radius r.

Answer: (x - h)^2 + (y - k)^2 = r^2

Question 11: Challenge: Given the circle x^2 + y^2 = 25, find all points on the circle where the x-coordinate is 3. Show detailed working.

Answer: y^2 = 25 - 9 = 16; y = ±4; points: (3, 4) and (3, -4)