Rolling Circle
A circle of varying radius moves in such a way that during its course of motion it always touches the -axis and also touches the fixed circle of radius units and centre at . What is the locus of the center of the moving circle?
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1 solution
If the centre of the circle is at the point ( x , y ) , then the radius of the circle is y and the distance from ( x , y ) to ( 0 , 3 ) is 2 + y , and hence x 2 + ( y − 3 ) 2 x 2 + 5 = ( y + 2 ) 2 = 1 0 y and so the locus of the centre of the circle is a parabola.
It is a little confusing to say a circle moves here, since its radius is changing all the time!