Question 1: Plot the locus of all points equidistant from point A (0,0) and point B (6,0).

Answer: A perpendicular bisector of AB passing through (3,0)

Question 2: Construct the locus of points 5 units from the circle centered at (2,2) with radius 3.

Answer: An outer circle with radius 8 and an inner circle with radius 2 centered at (2,2)

Question 3: Determine the locus of points 4 units from the line y=3.

Answer: Two lines y=3+4 and y=3−4

Question 4: Plot the points that are 3 units from point C (1,4) and also 4 units from point D (5,1).

Answer: Two intersection points of the circle centered at C with radius 3 and D with radius 4

Question 1: A lighthouse is located at (0,0). The coast runs along the x-axis. Plot the locus of points 10 km from the lighthouse that are also within 15 km of the coast. Describe the resulting region.

Answer: A circular region centered at (0,0) with radius 10, intersected with the band between y=−15 and y=15

Question 2: Construct the locus of all points that are equidistant from line y=2 and point (4,6).

Answer: A parabola with focus at (4,6) and directrix y=2

Question 3: A security camera is at (3,3). The camera's coverage area is all points exactly 5 units away. Plot this locus and explain how it can be used to determine the surveillance region.

Answer: A circle centered at (3,3) with radius 5; useful to check if a point is within the camera's range

Question 1: Construct the locus of points 4 units from a line segment AB of length 6, with A at (0,0) and B at (6,0).

Answer: Two lines parallel to AB, 4 units away at both sides

Question 2: Plot the intersection points of the loci: 3 units from point P (2,2) and 5 units from point Q (5,5).

Answer: Intersections of two circles with radii 3 and 5 centered at P and Q

Question 3: Explain why the locus of points 5 units from the circle centered at (0,0) with radius 4 is a concentric circle with radius 9.

Answer: Because all points 5 units from any point on the circle form a circle with radius 4+5=9

Question 1: Construct the locus of points that are simultaneously 4 units from line y=1 and from point (4,4). Describe its shape and significance.

Answer: A circle centered at (4,4) with radius 4, intersected with the pair of lines parallel to y=1 at 4 units away

Question 2: Given a point moving along a circle of radius 5 centered at (0,0), determine the locus of points 3 units from the moving point as it travels around the circle.

Answer: A torus (donut shape) formed by the set of points 3 units from the circle