document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=705215>Question 705215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not even sure what topic this problem falls under. It says, \"Find the standard form of the equation of the circle for which the endpoints of a diameter are (0,0)and (4, -6).<BR>\n" );
document.write( "Can you please help me with this?<BR>\n" );
document.write( "Thanks!<BR>\n" );
document.write( "Melissa </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #434463 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=434463\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If (0,0) and (4,-6) are endpoints of a diameter,<BR>\n" );
document.write( "the midpoint of that diameter is the center of the circle.<BR>\n" );
document.write( "Its coordinates are found by averaging the coordinates of those endpoints.<BR>\n" );
document.write( "The x-coordinate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B4%29%2F2=highlight%282%29 ALIGN=MIDDLE  ALT=\"%280%2B4%29%2F2=highlight%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The y-coordinate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B%28-6%29%29%2F2=highlight%28-3%29 ALIGN=MIDDLE  ALT=\"%280%2B%28-6%29%29%2F2=highlight%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, we have the center, C(2,-3).<BR>\n" );
document.write( " <BR>\n" );
document.write( "A picture is work a thousand words:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-2%2C6%2C-7%2C1%2C%0D%0Agrid%281%29%2C%0D%0Ared%28circle%282%2C-3%2Csqrt%2813%29%29%29%2C%0D%0Ablue%28circle%280%2C0%2C0.1%29%29%2Cblue%28circle%284%2C-6%2C0.1%29%29%2C%0D%0Ablue%28line%280%2C0%2C4%2C-6%29%29%2Cblue%28circle%282%2C-3%2C0.1%29%29%2C%0D%0Alocate%282.1%2C-3%2Cblue%28C%282%2C-3%29%29%29%2C%0D%0Agreen%28triangle%280.02%2C0.02%2C1.98%2C-3%2C0.02%2C-3%29%29%2C%0D%0Agreen%28rectangle%280.02%2C-3%2C0.22%2C-2.8%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The radius, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is the length of the segment form (0,0) to C(2,-3).<BR>\n" );
document.write( "That segment is the hypotenuse of a right triangle (drawn in green).<BR>\n" );
document.write( "We can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2 ALIGN=MIDDLE  ALT=\"R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > based on the Pythagorean theorem<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=2%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"R%5E2=2%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=4%2B9 ALIGN=MIDDLE  ALT=\"R%5E2=4%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2=highlight%2813%29 ALIGN=MIDDLE  ALT=\"R%5E2=highlight%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Any point (x,y) in the circle is at the same distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the center, C.<BR>\n" );
document.write( "As a consequence<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x-2%29%5E2%2B%28y%2B3%29%5E2=13%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x-2%29%5E2%2B%28y%2B3%29%5E2=13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );