SOLUTION: Each of a set of circles is tangent to y=3 and to x^2+y^2=1. Find the equation satisfied by the coordinates of the centers of these circles.

Question 1130620: Each of a set of circles is tangent to y=3 and to x^2+y^2=1. Find the equation satisfied by the coordinates of the centers of these circles.
Answer by greenestamps(13206) (Show Source): You can put this solution on YOUR website!

Let C(x,y) be the center of one of the circles that satisfy the given conditions.

The distance of C from the origin is

Every point on the given circle x^2+y^2=1 is 1 unit from the origin.

So the distance of C from the circle x^2+y^2=1 is

The distance of C from the line y=3 is

The required condition is that the distance of C from the circle x^2+y^2=1 be equal to the distance of C from the line y=3:

ANSWER: the equation of the locus of points that are centers of circles tangent to both x^2+y^2=1 and y=3 is

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