document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187485>Question 187485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a geometry question that is on my worksheet for my homework. My worksheet is labeled Distance in Coordinate Geometry. My question is Given circle O with O(3,-4) and radius 5, find 12 points on the circle with integer coordinates.\r<BR>\n" );
document.write( "\n" );
document.write( "I am stuck. I have been taught the formula for finding the equation of a circle which was tuaght to me like this:<BR>\n" );
document.write( "EXAMPLE: If the radius of a circle is 16 and the coordinates of the centerpoint are (3,4), then what is the equation?<BR>\n" );
document.write( "First, you put the x coordinate of the centerpoint into the first set of parantheses adn the y into the second set of parantheses. It should look like this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x-3%29%5E2%2B%28y-4%29%5E2=16%5E2+ ALIGN=MIDDLE  ALT=\"+%28x-3%29%5E2%2B%28y-4%29%5E2=16%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "I hope that this is clear enough. I get stuck here trying to figure out the coordinates of the points on the circle. I think that one of them is (8,-4). Are you suposed to just continue choosing random points to find the points, or is there an easier way? Please help, and thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140528 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=140528\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My question is Given circle O with O(3,-4) and radius 5, find 12 points on the circle with integer coordinates. <BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "(x-3)^2 + (y+4)^2 = 25<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "I think you will see the answer if you plot the center at (3,-4)<BR>\n" );
document.write( "Since the radius is \"5\" draw a radius to (0,0).<BR>\n" );
document.write( "Do you see the 3-4-5 right triangle with vertices at (0,0),<BR>\n" );
document.write( "(3,-4) and (0,-4)?<BR>\n" );
document.write( "If you do, plot the point (0,-8); it also forms a 3-4-5 rt.<BR>\n" );
document.write( "triangle with vertices (0,-4), (3,-4),(0.-8)<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Go up 5 from (3,-4) to (3,1).<BR>\n" );
document.write( "Go down5 from (3,-4) to (3,-9)<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "So far you have four solution points with integer values.<BR>\n" );
document.write( "Can you find the other 8?<BR>\n" );
document.write( "Consider the symmetry a circle has.<BR>\n" );
document.write( "-----------------------------------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );