Excerpt from Practical and Theoretical Geometry, Vol. 3

2. A fixed point O is joined to any point A on a given st. line which does not pass through O. P is a point on OA such that the ratio of OP to OA is constant. Find the locus of P.

3. A fixed point O is joined to any point A on the circumference of a given circle, P is a point on OA such that the ratio of OP to OA is constant. Find the locus of P.

Find the locus when P is on AO produced.

4. A fixed point O is joined to any point A on a given st. line which does not pass through O. P is a point on OA such that the rect. OP. OA is constant. Show that the locus of P is a circle.

Find the locus when P is on AO produced.

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