Question

A circle is tangent to the circle x^2 + y^2=4, x^2 +y^2=12+64. Find the locus of its center and draw the figure.

Answer 1

@geerky42

Answer 2

@perl

Answer 3

@phi

Answer 4

Two circles are tangent when they only touch at one point.
http://jwilson.coe.uga.edu/EMAT6680Su09/Park/As7dspark/As7dspark.html

"A locus is a set of points which satisfies a certain condition."
http://regentsprep.org/regents/math/geometry/gl1/what.htm

So if you think about it, the line that passes through the center of both circles will also pass through where they touch. That is the "locus of its center" as a line.

Some other notes on these:
http://mathworld.wolfram.com/TangentCircles.html