Interesting Loci Question Part 2

A circle has center (2,0) and radius 2 and P is any point on the circle. OP is produced to Q so that OQ=3OP. Find the equation of the locus of Q.

Here is a sketch of our situation:

Now, we can further points into the diagram:

The key trick in solving this question is similar triangles.

As OQ=3OP, we can say that the scale factor, k, is 3.

Now, as

So

This means that

So

Now, as h and k lie on the circle

Or alternatively,

Substituting

Then,

Clearing out the fractions,

So

This gives a circle, center (6,0) radius 6.

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