document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=897347>Question 897347</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are two concentric circles, whose areas are in the ratio 0.25. Determine the center if a straight line drawn from the center intersects the smaller and bigger circles at (2, 3) and (4, 8) respectively. \r<BR>\n" );
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document.write( "My answer is (0, -2). Am I correct? Please show me the working. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #544088 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><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=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=544088\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q:<BR>\n" );
document.write( "There are two concentric circles, whose areas are in the ratio 0.25. Determine the center if a straight line drawn from the center intersects the smaller and bigger circles at (2, 3) and (4, 8) respectively. <BR>\n" );
document.write( "My answer is (0, -2). Am I correct? Please show me the working.<BR>\n" );
document.write( "A:<BR>\n" );
document.write( "If (h,k) is the center of the circle, then the radius of the smaller circle is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28h-2%29%5E2%2B%28k-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28h-2%29%5E2%2B%28k-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the radius of the bigger circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28h-4%29%5E2%2B%28k-8%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28h-4%29%5E2%2B%28k-8%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The ratio of the area of the smaller circle to the area of the bigger circle is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28h-2%29%5E2%2B%28k-3%29%5E2%29%2F%28%28h-4%29%5E2%2B%28k-8%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28h-2%29%5E2%2B%28k-3%29%5E2%29%2F%28%28h-4%29%5E2%2B%28k-8%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28h-2%29%5E2%2B%28k-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28h-2%29%5E2%2B%28k-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.25<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28h-4%29%5E2%2B%28k-8%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28h-4%29%5E2%2B%28k-8%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by 4 and expand.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4h%5E2-16h%2B4k%5E2-24k%2B52 ALIGN=MIDDLE  ALT=\"4h%5E2-16h%2B4k%5E2-24k%2B52\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2-8h%2Bk%5E2-16k%2B80 ALIGN=MIDDLE  ALT=\"h%5E2-8h%2Bk%5E2-16k%2B80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2-8h%2B3k%5E2-8k-28+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2-8h%2B3k%5E2-8k-28+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The equation of the straight line is y = 2.5x - 2 so k = 2.5h - 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2-8h%2B3%282.5h+-+2%29%5E2-8%282.5h+-+2%29-28+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2-8h%2B3%282.5h+-+2%29%5E2-8%282.5h+-+2%29-28+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2-8h%2B3%286.25h%5E2-10h%2B4%29-20h-12+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2-8h%2B3%286.25h%5E2-10h%2B4%29-20h-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2-8h%2B18.75h%5E2-30h%2B12-20h-12+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2-8h%2B18.75h%5E2-30h%2B12-20h-12+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21.75h%5E2-58h+=+0 ALIGN=MIDDLE  ALT=\"21.75h%5E2-58h+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Multiply both sides by 4.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=87h%5E2-232h+=+0 ALIGN=MIDDLE  ALT=\"87h%5E2-232h+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Divide both sides by 29<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3h%5E2-8h+=+0 ALIGN=MIDDLE  ALT=\"3h%5E2-8h+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "h(3h - 8) = 0<BR>\n" );
document.write( "h = 0 or h = 8/3<BR>\n" );
document.write( "Using the equation k = 2.5h - 2.<BR>\n" );
document.write( "If h = 0, then k = -2.<BR>\n" );
document.write( "If h = 8/3, then k = 14/3.<BR>\n" );
document.write( "There are two possible answers.<BR>\n" );
document.write( "They are (0, -2) or (8/3, 14/3).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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