document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486499>Question 486499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. <BR>\n" );
document.write( "aV(0, 4), F(0, 3) <BR>\n" );
document.write( "bV(0, 1), F(0, 2) <BR>\n" );
document.write( "cV(4, 0), F(3, 0) <BR>\n" );
document.write( "dV(1, 0), F(2, 0) \r<BR>\n" );
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document.write( "2Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75. <BR>\n" );
document.write( "aC(–10, 0), r = 100 <BR>\n" );
document.write( "bC(–10, 0), r = 10 <BR>\n" );
document.write( "cC(–5, 0), r = 100 <BR>\n" );
document.write( "dC(–5, 0), r = 10 \r<BR>\n" );
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document.write( "3Find the foci of the ellipse with the following equation.<BR>\n" );
document.write( " ((x-1)ˆ2÷9)+((Y+2)ˆ2÷25)=1<BR>\n" );
document.write( "aF1(5, –2), F2(–3, –2) <BR>\n" );
document.write( "bF1(1, 2), F2(1, –6) <BR>\n" );
document.write( "cF1(4, –2), F2(–2, –2) <BR>\n" );
document.write( "dF1(1, 1), F2(1, –5) \r<BR>\n" );
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document.write( "4Find the slopes of the asymptotes of a hyperbola with the following equation.<BR>\n" );
document.write( " (Yˆ2÷81)-(xˆ2÷64)=1<BR>\n" );
document.write( "a8/9 <BR>\n" );
document.write( "b9/8 <BR>\n" );
document.write( "c8/9, –8/9 <BR>\n" );
document.write( "d9/8, –9/8  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332595 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=332595\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1Find the vertex and focus of the parabola whose equation is 4y = x2 + 4. <BR>\n" );
document.write( "2Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75. <BR>\n" );
document.write( "3Find the foci of the ellipse with the following equation.<BR>\n" );
document.write( "((x-1)ˆ2÷9)+((Y+2)ˆ2÷25)=1<BR>\n" );
document.write( "4Find the slopes of the asymptotes of a hyperbola with the following equation.<BR>\n" );
document.write( "(Yˆ2÷81)-(xˆ2÷64)=1<BR>\n" );
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document.write( "1) Find the vertex and focus of the parabola whose equation is 4y = x^2 + 4.<BR>\n" );
document.write( "y=x^2/4+4/4<BR>\n" );
document.write( "y=x^2/4+1<BR>\n" );
document.write( "y=(1/4)(x^2)+1<BR>\n" );
document.write( "x^2/4=y-1<BR>\n" );
document.write( "x^2=4(y-1)<BR>\n" );
document.write( "This is an equation of a parabola of standard form: (x-h)^2=4p(y-k), (h, k) being the (x, y) coordinates of the vertex. Parabola has a vertical axis of symmetry and it opens upwards.<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "vertex: (0,1)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "4p=4<BR>\n" );
document.write( "p=1<BR>\n" );
document.write( "focus: (0,2)<BR>\n" );
document.write( "ans:bV(0, 1), F(0, 2) <BR>\n" );
document.write( "..<BR>\n" );
document.write( "2) Find the center and radius of the circle whose equation is x2 + 10x + y2 = 75.<BR>\n" );
document.write( "x^2+10x+y^2=75<BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "(x^2+10x+25)+(y^2)=75+25=100<BR>\n" );
document.write( "(x+5)^2+(y+0)^2=100<BR>\n" );
document.write( "center:(-5,0)<BR>\n" );
document.write( "radius=&#8730;100=10<BR>\n" );
document.write( "ans:dC(–5, 0), r = 10<BR>\n" );
document.write( "..<BR>\n" );
document.write( "3) Find the foci of the ellipse with the following equation.<BR>\n" );
document.write( "((x-1)ˆ2/9)+((Y+2)ˆ2/25)=1<BR>\n" );
document.write( "This is an equation of an ellipse with vertical major axis of the standard form: <BR>\n" );
document.write( "(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "center: (1,-2)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "c^2=a^2-b^2=25-9=16<BR>\n" );
document.write( "c=&#8730;16=4<BR>\n" );
document.write( "Foci: (1,-2ħc)=(1,-2ħ4)=(1,2) and (1,-6)<BR>\n" );
document.write( "ans: bF1(1, 2), F2(1, –6)<BR>\n" );
document.write( "..<BR>\n" );
document.write( "4Find the slopes of the asymptotes of a hyperbola with the following equation.<BR>\n" );
document.write( "(Yˆ2/81)-(xˆ2/64)=1<BR>\n" );
document.write( "This is an equation of a hyperbola with vertical transverse axis of the standard form:<BR>\n" );
document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center<BR>\n" );
document.write( "For given equation:<BR>\n" );
document.write( "Center: (0,0)<BR>\n" );
document.write( "a^2=81<BR>\n" );
document.write( "a=&#8730;81=9<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b^2=64<BR>\n" );
document.write( "b=&#8730;64=8<BR>\n" );
document.write( "slope of asymptotes=ħa/b=ħ9/8<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "d9/8, –9/8 </SPAN>\n" );
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