document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192942>Question 192942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I got this question on a test and i missed it<BR>\n" );
document.write( "its about locus of points...\r<BR>\n" );
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document.write( "ther are 4 of them and i dont understand them at all!!\r<BR>\n" );
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document.write( "draw a sketch and write the equation for each locus<BR>\n" );
document.write( "but i think i only really need the equation \r<BR>\n" );
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document.write( "the first says\r<BR>\n" );
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document.write( "locus of points equidistant from y= x+4 and passing through y=1 and y=7\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "locus of points equidistant from (3,4) and (3,-2)\r<BR>\n" );
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document.write( "3.<BR>\n" );
document.write( "locus points 5 units from origin \r<BR>\n" );
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document.write( "4.<BR>\n" );
document.write( "locus of points 3 units from origin\r<BR>\n" );
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document.write( "and then there are 2 more from a different test.\r<BR>\n" );
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document.write( "83.<BR>\n" );
document.write( "locus of points 4 units away from x= -2\r<BR>\n" );
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document.write( "84.<BR>\n" );
document.write( "locus of point equidistant from y= -x+2 passing through y=4 and y=0.\r<BR>\n" );
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document.write( "if someone could help me i would be so thankful.  homeschool and move alot so its hard for me to get help on my work. this site is a life saver!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144806 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=144806\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> locus  problems  are  great  if  you  are  good  at  visualization\r<BR>\n" );
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document.write( "loci  around  a  point  is  a  circle  in  a  plane,  and  a  sphere  in  space  ok?\r<BR>\n" );
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document.write( "loci  of  2  points  is  a  line  perpendicular  to  connecting  line  thru  midpoint,  in  a  plane.\r<BR>\n" );
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document.write( "In  space  this  is  harder  to  describe.  visualize  a  sphere  around  one  point,  and  then  another  sphere  of  same  size  around  other point.  If  spheres  just  touch,  it  is  a  point.  If  they   merge  together  more,  it  is  circular  plane.\r<BR>\n" );
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document.write( "loci  around  a  line,  is  just  two  parallel  lines  equidistant  from  original  line,  in  a  plane.\r<BR>\n" );
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document.write( "in  space,   it  is  like  a  hollow  tube,cylindrical  surface,   with the  line  as  the  center  axis\r<BR>\n" );
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document.write( "1)  Similar  to  #  84<BR>\n" );
document.write( "remember  loci  in a  plane  of  a  line  are  parallel  lines  at  equal  distances  from  line.<BR>\n" );
document.write( "Your  problem  did  not  specify  how  far  apart,  so  we  will  just  be  convenient.  you  can  modify  to  suit.\r<BR>\n" );
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document.write( "original  line  is  y=x+4,  draw  a  rough  sketch.  x-y  coordinates.  y  intersect  at  4,  that  is  (0,4) point.   slope  is  +1.  IF  we  choose  a  line  parallel  to  this  but  3  units  to  right,  we  have  y=x+1.  <BR>\n" );
document.write( "And  the  counterpart,  3  units  to  left  is  , y=x+7 \r<BR>\n" );
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document.write( "at  y=1,  our  loci  coordinates  are, (0,1)  and  (-6,1),,original (-3,1)<BR>\n" );
document.write( "at  y=7,  loci,,(6,7)  and (0,7),,original  (3,7)\r<BR>\n" );
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document.write( "2)  the  midpoint  between  (3,4)  and  (3,-2)  is  (3,1)  and  line  perpendicluar  to  connecting  line  is  <BR>\n" );
document.write( "y=(+1)    Easier  to  just  sketch  roughly\r<BR>\n" );
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document.write( "3)loci  is  circle  of  radius  5  about  origin.  x^2+y^2=25    again  sketch  helps\r<BR>\n" );
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document.write( "4)  same  as  (3)  but  radius  =3,  x^2 +y^2 =9\r<BR>\n" );
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document.write( "have  you  studied  equation  for  circle  is  x^2+y^2=radius ^2\r<BR>\n" );
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document.write( "83)  sketch  helps,  original  line  ,,x=(-2),  is  a  vertical  line  thru  (-2,0)\r<BR>\n" );
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document.write( "loci  4  units  to  right  is  x=(+2),  and  4  units  to  left  is, x=(-6)<BR>\n" );
document.write( "Again  both  are  vertical  lines,  parallel  to  original\r<BR>\n" );
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document.write( "84)  Again,  similar  to  (1)\r<BR>\n" );
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document.write( "sketching  the  original  line,  y  intercept is  (0,2),,slope(-1)  y=-x+2\r<BR>\n" );
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document.write( "loci  lines  are  parallel  and  equidistant,  but  again  we  do  not  know  how  far\r<BR>\n" );
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document.write( "lets  use  a  transfer  3  right  or  left  again<BR>\n" );
document.write( "original  eqn,  y=-x+2,  to left  eqn  y=-x-1,  to  right  y=-x+5\r<BR>\n" );
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document.write( "generating  coordinates  we  find  original (2,0)  right (5,0),,  left  (-1,0)\r<BR>\n" );
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document.write( "likewise   (-2,4),  (1,4),  (-5,4)\r<BR>\n" );
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document.write( "Hopefully  this  is  close  to  your  needs </SPAN>\n" );
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