document.write( "Question 169559: A moving circle is tangent to the x-axis and to a circle of radius one with center at (2,-6). Find the equation of the locus of the center of the moving circle. \n" ); document.write( "

Algebra.Com's Answer #125086 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!
Warning: Alan's equation
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\n" ); document.write( "\n" ); document.write( "A moving circle is tangent to the x-axis and to a circle of radius one with center at (2,-6). Find the equation of the locus of the center of the moving circle.
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document.write( "Let's draw the given circle with center (2,-6) and radius 1.\r\n" );
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document.write( "Next let's draw in any arbitrary circle which is tangent \r\n" );
document.write( "to both that circle and the x-axis and label its center \r\n" );
document.write( "as the general point (x,y) :\r\n" );
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document.write( "Draw a line segment connecting the center of this circle\r\n" );
document.write( "(x,y), to the center of the given circle.\r\n" );
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document.write( "Use the distance formula to find an expression\r\n" );
document.write( "for the distance between them:\r\n" );
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document.write( "That distance is the radius of the arbitrary circle\r\n" );
document.write( "plus 1.\r\n" );
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document.write( "Now let's draw a radius of the arbitrary circle \r\n" );
document.write( "vertically up to the x-axis.\r\n" );
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document.write( "That vertical radius of the arbitrary circle must \r\n" );
document.write( "equal to -y in length because y must be negative, \r\n" );
document.write( "and so -y must be positive.\r\n" );
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document.write( "Distance between centers = \r\n" );
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document.write( "          radius of arbitrary circle +\r\n" );
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document.write( "                      radius of the given circle.\r\n" );
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document.write( "So \r\n" );
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document.write( "Squaring both sides:\r\n" );
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document.write( "That is the equation you are looking for.\r\n" );
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document.write( "Now let's draw the graph of that.\r\n" );
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document.write( "It is obviously a parabola opening\r\n" );
document.write( "downward:\r\n" );
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document.write( "Notice that any point we pick on that parabola,\r\n" );
document.write( "draw a circle with that center tangent to the x-axis, \r\n" );
document.write( "it will automatically be tangent to the given circle:\r\n" );
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document.write( "Edwin

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