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

Answer: 5

Question 2: Write the equation of a circle with center at (3, -2) and radius 4.

Answer: (x - 3)² + (y + 2)² = 16

Question 3: Plot the graph of y = 2x on the grid.

Answer: Students will draw the line y=2x on the grid.

Question 4: Construct a circle with center at (0,0) passing through the point (3,4).

Answer: Radius = 5; equation: x² + y² = 25

Question 1: Determine the equation of the circle with center at (2, -3) and passing through (5, 1).

Answer: (x - 2)² + (y + 3)² = 25

Question 2: A circle has its center at (4, 5) and passes through (7, 9). Find its equation and radius.

Answer: (x - 4)² + (y - 5)² = 25

Question 3: Explain why all points on a circle are equidistant from the center, and how this relates to the concept of a locus.

Answer: All points on a circle are at a fixed distance (radius) from the center because by definition, a circle is the locus of all points that are constantly equidistant from a fixed point.

Question 4: Given the equation x² + y² - 6x + 4y + 9 = 0, find the center and radius of the circle.

Answer: Center: (3, -2), Radius: √10

Question 5: Describe how the equation of a circle changes if its center is moved from (0,0) to (h, k).

Answer: The equation becomes (x - h)² + (y - k)² = r², shifting the circle's center to (h, k).

Question 1: A round table has a radius of 1.5 meters. If a circular rug is to be placed under it with the same center, what is the equation of the rug? (Center at origin)

Answer: x² + y² = 2.25

Question 2: A drone is flying around a point at (4, 4) maintaining a constant distance of 10 meters. Write the equation describing its flight path.

Answer: (x - 4)² + (y - 4)² = 100

Question 1: Given a circle with equation x² + y² + 4x - 6y + 9 = 0, find its center and radius. Then, determine if the point (0,0) lies inside, on, or outside the circle.

Answer: Center: (-2, 3), Radius: √10; point (0,0) is outside.

Question 2: Construct a circle with a diameter from (1,2) to (5,6). What is the equation of the circle?

Answer: Center at (3,4), radius √8, equation: (x - 3)² + (y - 4)² = 8

Question 1: Find the equation of a circle with center at (0,0) and passing through (0,7).

Answer: x² + y² = 49

Question 2: Plot the circle (x - 2)² + (y + 3)² = 16 on the grid and describe its position.

Answer: Circle with center at (2, -3) and radius 4.

Question 1: A student wrote the equation of a circle as x² + y² + 4x - 6y + 9 = 0 and concluded its radius is 3. Is this correct? If not, find the correct radius.

Answer: Incorrect; the radius is √10, approximately 3.16.