document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428548>Question 428548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with these problems.  I need to know how to work it out, not just the answer, so I can figure out others.\r<BR>\n" );
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document.write( "1:  Plans to build a park include a circular fountain.  The outline of the fountain can be modeled with the equation (x-4)^2+(y+5)^2=50, where the units are meters and the graph is on a grid map of the park. Find the coordinates of the center of the fountain AND find the circumference of the fountain.\r<BR>\n" );
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document.write( "2:  Bill is making a graphic design on the computer using a coordinate grid.  He starts with a circle with center (0,0).  He then draws a congruent circle with the equation x^2+y^2+12x+4y+5=0.  What was the radius of the first circle and what translation did he make to draw the second circle?\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297854 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1: Plans to build a park include a circular fountain. The outline of the fountain can be modeled with the equation (x-4)^2+(y+5)^2=50, where the units are meters and the graph is on a grid map of the park. Find the coordinates of the center of the fountain AND find the circumference of the fountain.<BR>\n" );
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document.write( "The center is at (4,-5)<BR>\n" );
document.write( "The radius = sqrt(50) = 5sqrt(2)<BR>\n" );
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document.write( "Circum = 2(pi)r = 2(pi)5sqrt(2) = 10(pi)sqrt(2)<BR>\n" );
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document.write( "2: Bill is making a graphic design on the computer using a coordinate grid. He starts with a circle with center (0,0). He then draws a congruent circle with the equation x^2+y^2+12x+4y+5=0. What was the radius of the first circle and what translation did he make to draw the second circle?<BR>\n" );
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document.write( "Complete the square:<BR>\n" );
document.write( "x^2+12x+a + y^2+4y+b = -5+a+b<BR>\n" );
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document.write( "x^2+12x+36 + y^2+4y+4 = -5+36+4<BR>\n" );
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document.write( "(x+6) + (y+2) = 35<BR>\n" );
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document.write( "Center at (-6,-2); radius = sqrt(35)<BR>\n" );
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document.write( "Radius of the 1st circle was sqrt(35)<BR>\n" );
document.write( "Translation: He moved the 1st circle 6 to the left<BR>\n" );
document.write( "and 2 down.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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