document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094135>Question 1094135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of two circles which pass through point (2, 0) that have both Y-axis and the line y-1 =0 as the tangent.\r<BR>\n" );
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document.write( "am sorry to asked this question but I need your help.<BR>\n" );
document.write( "thank  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708763 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>To be tangent to the y-axis (the line x=0) and the line y-1=0 (i.e., y=1), the center of the circle must be equidistant from x=0 and y=1.  The set of points equidistant from x=0 and y=1 is the line with slope -1 passing through (0,1), the intersection point of lines y=1 and x=0.<br><BR>\n" );
document.write( "The equation of that line is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%2B1 ALIGN=MIDDLE  ALT=\"y+=+-x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So an arbitrary point on that line will have coordinates (a,-a+1).  The distance of any such point from the y-axis is clearly equal to a.  For the circle to pass through the point (2,0), the distance between (a,-a+1) and (2,0) must also be equal to a.  Since the distances need to be the same, the squares of the distances need to be the same.  So<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-6a%2B5+=+0 ALIGN=MIDDLE  ALT=\"a%5E2-6a%2B5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-5%29%28a-1%29+=+0 ALIGN=MIDDLE  ALT=\"%28a-5%29%28a-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The x coordinates of the centers of the two circles are 5 and 1.  For the circle with center x coordinate 1, the y coordinate is (-1+1) = 0; for the other circle, the y coordinate is (-5+1) = -4.  So the centers of the two circles are (1,0) and (5,-4).<br><BR>\n" );
document.write( "Since the circles are tangent to the y axis, the radius of each is the x coordinate of the center.  So the two circles are<BR>\n" );
document.write( "(1) center (1,0), radius 1  and<BR>\n" );
document.write( "(2) center (5,-4), radius 5.<br><BR>\n" );
document.write( "The equations are then<BR>\n" );
document.write( "(1) (x-1)^2+y^2 = 1  and<BR>\n" );
document.write( "(2) (x-5)^2 + (y+4)^2 = 25<BR>\n" );
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