HW HELP PLEASE

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I have no idea what to do...please help.

1) Find the locus of the centers of circles which are tangent to the y-axis and to the circle x^2 + y^2 = 2rx.



2) The vertex of a triangle is fixed at the point (0,a) and the base is a segment of the x-axis of length 2a. Find the locus of the center of the circle circumscribed about the triangle.
 
\(\displaystyle x^2+y^2=2rx\)

A circle equation is

\(\displaystyle (x-x_c)^2+(y-y_c)^2=r^2\)

\(\displaystyle where\ the\ centre\ is\ \ \ (x_c,y_c)\)

If you multiply out the circle equation in brackets, you have

\(\displaystyle x^2,\ y^2, x\ and\ y\ terms.\)

Are there any \(\displaystyle \ \ y\ \\) terms in your original expression??

What does that tell you about the y co-ordinate of the centres of all those circles????

The second one is a nice piece of geometry,
so if you genuinely apply yourself to the first one, we can go through the 2nd.
 
\(\displaystyle x^2+y^2=2rx\)

\(\displaystyle x^2-2rx+y^2=0\)

\(\displaystyle x^2-2rx+(rx)^2+y^2=(rx)^2\)

\(\displaystyle (x-rx)^2+(y-0)^2=(rx)^2\)

This is a circle, centre (rx,0), radius R=rx

If r is allowed to be a positive or negative variable, then the x-axis is the locus.
 
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