document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421697>Question 421697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need a lot of help with these questions i do not understand them at all..! pleas help.! \r<BR>\n" );
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document.write( "1.What is the distance between the following points?<BR>\n" );
document.write( "(-2 sq root 7,10) (4 sq rt 7,8)<BR>\n" );
document.write( "2.What is the axis of symmetry of the parabola with the equation x – 4 = 1/4(y + 1)2<BR>\n" );
document.write( "3.Find the foci of an ellipse with the equation 7(x – 2)2 + 3(y – 2)2 = 21.<BR>\n" );
document.write( "4.Find the vertices of a hyperbola with the equation (x + 3)2 – 4(y – 2)2 = 4<BR>\n" );
document.write( "5.Find the foci of a hyperbola with the equation 9y2 – 72y – 16x2 – 64x – 64 = 0\r<BR>\n" );
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document.write( "i need the last few to be in (a,b) form.. Thanks.!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294496 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=294496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.What is the distance between the following points?<BR>\n" );
document.write( "(-2 sq root 7,10) (4 sq rt 7,8)<BR>\n" );
document.write( "2.What is the axis of symmetry of the parabola with the equation<BR>\n" );
document.write( " x – 4 = 1/4(y + 1)2<BR>\n" );
document.write( "3.Find the foci of an ellipse with the equation 7(x – 2)2 + 3(y – 2)2 = 21.<BR>\n" );
document.write( "4.Find the vertices of a hyperbola with the equation (x + 3)2 – 4(y – 2)2 = 4<BR>\n" );
document.write( "5.Find the foci of a hyperbola with the equation 9y2 – 72y – 16x2 – 64x – 64 = 0 ..\r<BR>\n" );
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document.write( "1.The formula for finding distance between two points:<BR>\n" );
document.write( "d=sqrt[(x1-x2)^2+(y1-y2)^2]<BR>\n" );
document.write( "for given points, <BR>\n" );
document.write( "distance=sqrt[(4sqrt7-(-2sqrt7))^2+(8-10)^2]<BR>\n" );
document.write( "=sqrt[(6sqrt7)^2+(-2)^2]<BR>\n" );
document.write( "=sqrt[252+4]=sqrt256=16 (ans)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "2.x–4=1/4(y+1)2<BR>\n" );
document.write( "This can be rewritten:<BR>\n" );
document.write( "x-4=1/2(y+1)^2<BR>\n" );
document.write( "or x=1/2(y+1)^2+4<BR>\n" );
document.write( "This is now written in standard form of a parabola, x=A(y-k)^2+h, with (h,k) being the (x,y) coordinates of the parabola.<BR>\n" );
document.write( "For the given equation, this is a parabola that opens sideways to the right, with the vertex at (4,-1). The axis of symmetry is y=-1<BR>\n" );
document.write( "The graph below will help you understand what some of the numbers above represent: <BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=-1+-(2x-8)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-2%2C+10%2C+-5%2C+5%2C+-1%2B%282x-8%29%5E.5%2C-1-%282x-8%29%5E.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+200%2C+200%2C+-2%2C+10%2C+-5%2C+5%2C+-1%2B%282x-8%29%5E.5%2C-1-%282x-8%29%5E.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "3. 7(x–2)^2+3(y–2)^2=21<BR>\n" );
document.write( "   Standard form for an ellipse:(x-h)^2/a^2+(y-k)^2/b^2      <BR>\n" );
document.write( "   or(y-k)^2/a^2+(x-h)^2/b^2,a>b<BR>\n" );
document.write( "   for given equation, divide by 21 to write it in standard form,<BR>\n" );
document.write( "   (x–2)^2/3+(y–2)^2/7=1 (Since the denominator of the y^2-term is greater than    <BR>\n" );
document.write( "   the denominator of the x^2-term, the given equation is of the second standard  <BR>\n" );
document.write( "   form listed above.)<BR>\n" );
document.write( "   (y–2)^2/7+(x–2)^2/3=1<BR>\n" );
document.write( "   This an ellipse with center at (2,2) with vertical major axis.<BR>\n" );
document.write( "   a^2=7<BR>\n" );
document.write( "   a=sqrt7<BR>\n" );
document.write( "   b^2=3<BR>\n" );
document.write( "   b=sqrt3<BR>\n" );
document.write( "   c^2=a^2-b^2=7-3=4<BR>\n" );
document.write( "   c=sqrt4=2<BR>\n" );
document.write( "   foci=+-c from the center on the vertical major axis<BR>\n" );
document.write( "   =(2,4) and (2,0)<BR>\n" );
document.write( "   The graph of the given ellipse below may help you understand some of the<BR>\n" );
document.write( "   numbers I came up with:<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=2+-(7-(7/3)(x-2)^2)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-5%2C+5%2C+-2%2C+5%2C+2%2B%287-%287%2F3%29%28x-2%29%5E2%29%5E.5%2C2-%287-%287%2F3%29%28x-2%29%5E2%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "..<BR>\n" );
document.write( "4.Find the vertices of a hyperbola with the equation (x+3)^2–4(y–2)^2=4\r<BR>\n" );
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document.write( "(x+3)^2–4(y–2)^2=4<BR>\n" );
document.write( "Standard form of a hyperbola: (x-h)^2/a^2-(y-k)^2/b^2=1. Notice this form is almost as same as that of an ellipse except a hyperbola has a negative second term.  <BR>\n" );
document.write( "Divide given equation by 4,<BR>\n" );
document.write( "(x+3)^2/4–(y–2)^2/1=1<BR>\n" );
document.write( "This is a hyperbola with center at (-3,2) and it has a horizontal transverse axis at y=2, that is, it opens sideways.<BR>\n" );
document.write( "a^2=4<BR>\n" );
document.write( "a=2<BR>\n" );
document.write( "b^2=1<BR>\n" );
document.write( "b=1<BR>\n" );
document.write( "c^2=a^2+b^2<BR>\n" );
document.write( "c=sqrt(4+1)=sqrt(5)=2.24<BR>\n" );
document.write( "vertices on the transverse axis=-3+-a=(-5,2) and (-1,2)<BR>\n" );
document.write( "Foci on the transverse axis=-3+-c=-3+-2.24=(-5.24,2) and (.76,2)<BR>\n" );
document.write( "The graph of the given hyperbola below could serve as a check on some of the numbers like the center, vertices and foci.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y=2+-((x+3)^2/4-1)^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-10%2C+5%2C+-5%2C+5%2C+2%2B%28%28x%2B3%29%5E2%2F4-1%29%5E.5%2C2-%28%28x%2B3%29%5E2%2F4-1%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "..<BR>\n" );
document.write( "5.Find the foci of a hyperbola with the equation 9y2–72y–16x2–64x–64=0 <BR>\n" );
document.write( "9y2–72y–16x2–64x–64=0<BR>\n" );
document.write( "you need to complete the square before you can see it in standard form:\r<BR>\n" );
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document.write( "9(y2–8y+16)–16(x2+4x+4)=64+144-64=144<BR>\n" );
document.write( "9(y-4)^2-16(x+2)^2=144<BR>\n" );
document.write( "Divide by 144<BR>\n" );
document.write( "(y-4)^2/16-(x+2)^2/9=1<BR>\n" );
document.write( "This is a hyperbola with center at (-2,4) with a vertical transverse axis,x=-2, that is it opens up and down.<BR>\n" );
document.write( "a^2=16<BR>\n" );
document.write( "a=4<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=3<BR>\n" );
document.write( "c=sqrt(a^2+b^2)=sqrt(25)=5 <BR>\n" );
document.write( "On the vertical transverse axis,<BR>\n" );
document.write( "foci:(-2,4+-c)=(-2,4+-5)=(-2,9) and (-2,-1)<BR>\n" );
document.write( "The graph below can serve as a check on the center and foci.\r<BR>\n" );
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document.write( "..<BR>\n" );
document.write( "y=4+-(16(1+(x+2)^2/9))^.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+200%2C+200%2C+-5%2C+5%2C+-5%2C+10%2C+4%2B%2816%281%2B%28x%2B2%29%5E2%2F9%29%29%5E.5%2C4-%2816%281%2B%28x%2B2%29%5E2%2F9%29%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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