Question 1: Given a circle with center O at (3, 4) and radius 5, plot the circle on the grid.

Answer: Centered at (3,4) with radius 5

Question 2: Calculate the diameter of a circle with radius 7.

Answer: 14

Question 3: If a point P is 4 units from the center of a circle, what is the length of the radius if P lies outside the circle?

Answer: 4 plus the radius

Question 1: A circle has a radius of 6 cm. A point P is 8 cm from the center. Is point P inside, outside, or on the circle? Justify your answer.

Answer: outside

Question 2: Construct a circle with center at (2, 3) passing through point (6, 7). Calculate its radius and plot the circle.

Answer: Radius = 4√2 units

Question 1: A circular garden has a diameter of 12 meters. A path runs along the circumference. Calculate the length of the path.

Answer: Approx. 37.7 meters

Question 2: A bicycle wheel has a radius of 35 cm. How far does the wheel travel in 10 rotations?

Answer: Approx. 220 meters

Question 1: Construct a circle with a center at (0, 0) passing through (3, 4). Then, find and explain the length of the radius and the equation of the circle.

Answer: Radius = 5; Equation: x^2 + y^2 = 25

Question 2: Given a circle with equation x^2 + y^2 - 6x + 4y + 9 = 0, find the center and radius, then draw the circle on the grid.

Answer: Center at (3, -2), Radius = √(4+16) = √20

Question 1: A student draws a circle with center at (5, 5) and claims the radius is 3 units, but the circle passes through point (8, 5). Is the student's claim correct? Explain and correct if necessary.

Answer: Incorrect; radius should be 3 units, but point (8, 5) is 3 units from (5,5), so the claim is actually correct.

Question 2: A student calculates the radius of a circle as 10 units using the formula r = √(x2 - x1)^2 + (y2 - y1)^2, but makes a mistake in the formula. Identify the mistake and write the correct formula.

Answer: Incorrect; correct formula is r = √[(x2 - x1)^2 + (y2 - y1)^2]