Locuses

Apr 2010
5
0
Can you help me with these problems, I am having a hard time vizualizing them.

1. What is the locus in space of points equidistant from all the points on a given circle

2. find the locus of the centers of all circles of all circles that pass through the points

3. What is the name of the surface in space every point of which is a fixed distance from a given line

4. a circle with a given radius rolls along the perimeter of a equilateral triangle. what is the locus

5. given a circle with center P and a radius of 10 cm find the locus of the midpoints of all possible 12 cm chords in the circle.
 

Grandad

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Dec 2008
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Hello lamas9000
Can you help me with these problems, I am having a hard time vizualizing them.

1. What is the locus in space of points equidistant from all the points on a given circle
There's only one point that's equidistant from all the points on a given circle: the centre of the circle.

2. find the locus of the centers of all circles of all circles that pass through the points
This doesn't make sense.

3. What is the name of the surface in space every point of which is a fixed distance from a given line
A cylinder whose axis is the given line, radius the fixed distance.

4. a circle with a given radius rolls along the perimeter of a equilateral triangle. what is the locus
What is the locus of what? This is incomplete.

5. given a circle with center P and a radius of 10 cm find the locus of the midpoints of all possible 12 cm chords in the circle.
Draw a diagram showing one such chord; join its mid-point to the centre P of the circle. Using Pythagoras' Theorem, the distance of this mid-point from P is 8 cm. So the locus is a circle, centre P, radius 8 cm.

Grandad