Help with some homework questions?

Question

Please give me a brief explanation of how you got these answers so I'll be better at in the future. Thanks. :)

1.) Which doesn't represent a possible intersection of a line and a right cone with height 4 cm: 3 points, 2 points, or one point?

2.) Describe the locus of all points in a plane that are 9 cm from M?
circle M with a radius of 18 cm
circle M with a radius of 9 cm
square with 9 cm sides
square with 18 cm sides

3.) Describe the locus of all points that are 3 cm from a point m?

a line, 3 cm from line m
a pair of parallel lines, each parallel to and 3 cm from line m
a sphere with a radius of 3 cm
a circle with a diameter of 6 cm

I really don't get that locus stuff, if someone could explain I'd feel smarter lol. :)

Answer 1

The key to locus problems is being able to visualize things.

(1) If you cross a line with a cone, they can meet at one point (the vertex of the cone or one point on the base). They can meet at two points if the line goes through the cone. There's no way a line can meet a cone at exactly three points, though.

(2) All points on a plane a certain distance from a given point form a circle. The radius is the distance the points are away from the center. This one is a circle with a radius of 9 cm.

(3) Because we're not limited to a plane, all points a certain distance away from a given point form a sphere.

Answer 2

3 points

circle M with radius 9 cm

sphere m with radius of 3 cm

Answer 3

answer on ques. (2)
circle M with a radius of 9 cm