document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44360>Question 44360</A>: <I><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
document.write( "1.What is the equation of the directrix of the parabola with equation x=4y2+16y+19?\r<BR>\n" );
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document.write( "2. What is the length of the major axis of the ellipse with equation 4(x+4)2+9(y-1)2+36?\r<BR>\n" );
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document.write( "3. What are the foci of the ellipse with equation x2+4y2=36?\r<BR>\n" );
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document.write( "4. What are the slpoes of the asymptotes of the hyperbola with equation 4x2-y2+8x-6y=9? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29301 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=29301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.What is the equation of the directrix of the parabola with equation x=4y2+16y+19? <BR>\n" );
document.write( "x-19+16=4(y^2+4y+4)<BR>\n" );
document.write( "x-3=4(y+2)^2<BR>\n" );
document.write( "(y+2)^2=(1/4)(x-3)<BR>\n" );
document.write( "Vertex is at (3,-2); 4p=1/4 so p=1/16;<BR>\n" );
document.write( "Parabola opens to the right so the directrix is 1/16 to the left of the <BR>\n" );
document.write( "vertex.  Directrix is x=3-(1/16)=47/16<BR>\n" );
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document.write( "2. What is the length of the major axis of the ellipse with equation 4(x+4)^2+9(y-1)^2=36? <BR>\n" );
document.write( "Dividing through by 36 get;<BR>\n" );
document.write( "[(x+4)^2/9] + [(y-1)^2/4] = 1\r<BR>\n" );
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document.write( "a=3 so the length of the major axis is 2a=6<BR>\n" );
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document.write( "3. What are the foci of the ellipse with equation x^2+4y^2=36?<BR>\n" );
document.write( "Divide through by 36 to get;<BR>\n" );
document.write( " [x^2/36] +[y^2/9] = 1<BR>\n" );
document.write( " a=6, b=3<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "c=sqrt(27)=3sqrt3<BR>\n" );
document.write( "Center is at (0,0)<BR>\n" );
document.write( "So Foci are at (c,0), (-c,0)<BR>\n" );
document.write( "Foci: (3sqrt3,0) (-3sqrt3,0)<BR>\n" );
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document.write( "4. What are the slopes of the asymptotes of the hyperbola with equation     4x2^-y2+8x-6y=9?\r<BR>\n" );
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document.write( "4x^2+8x-(y^2+6y)=9<BR>\n" );
document.write( "4(x^2+2x+1)-(y^2+6y+9)=9+4-9<BR>\n" );
document.write( "(x+1)^2-[(y+3)^2]/4 =1<BR>\n" );
document.write( "Center is at (h,k)=(-1,-3)<BR>\n" );
document.write( "a=1;b=2<BR>\n" );
document.write( "c^2=a^2+b^2=5; so c=sqrt5<BR>\n" );
document.write( "Asymptote forms are y-k=(b/a)(x-h) and y-k=-(b/a)(x-h)<BR>\n" );
document.write( "I'll let you make the proper substitutions.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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