geometry homework!!!!

Question

1) Describe the Locus  of all points in space that are equidistant from all of the points on a circle  .

2) A torus is a doughnut-shaped solid that can be described as the locus of all points in space that are a given distance from what type of plane curve?

3) Find the locus of all points in a coordinate plane that are equidistant from points (-3,0) and  (0,3).

4) Describe the cross section obtained when a plane intersects a sphere of radius 4in., through its center.

5) If the diameter of a spherical ball is doubled , by what factor does its surface area increase?

Answer 1

1a) A "locus" is a basically a set of points that match a certain description.

b) For example, you know that a circle is the set (or "locus") of points the same distance from a fixed point (the center).

c) The sphere that has a center is the point and whose radius is the constant equal distance is called circle.

2a) A circle with radius equal to the given distance that is centered at the point, in a plane perpendicular to the plane of the original circle.

b) If you do that for every point on the original circle, you will have a torus.

3) Let (x,y) be a point

Squared distance between (x,y) and (-3,0) = (x+3)^2+y^2

Squared distance between (x,y) and (0,3) = x^2+(y-3)^2

 

(x+3)^2+y^2=x^2+(y-3)^2

 

x^2+6x+9+y^2 = x^2+y^2-6y+9

 

6x=-6y

 

The line y=-x

 

Answer 2

since diameter is doubled.

Substitute known vales

surface area will be increased by 4 times.

Answer 3

4).

A plane through the sphere center is like slicing an orange in half.
The cross section would be a circle with the radius of the circle equal to the radius of the sphere (4 in).