document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319357>Question 319357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.Find the center and radius of the circle whose equation is x2 + 10x + y2= 75. <BR>\n" );
document.write( "a. C(–10, 0), r = 100 <BR>\n" );
document.write( "b.  C(–10, 0), r = 10 <BR>\n" );
document.write( "c.  C(–5, 0), r = 100 <BR>\n" );
document.write( "d.  C(–5, 0), r = 10 <BR>\n" );
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document.write( "5. Find the foci of the ellipse with the following equation.<BR>\n" );
document.write( "(x - 1)^2/9  +  (y+2)^2/25 =1<BR>\n" );
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document.write( "A. F1(5, –2), F2(–3, –2) <BR>\n" );
document.write( "b. F1(1, 2), F2(1, –6) <BR>\n" );
document.write( "c. F1(4, –2), F2(–2, –2) <BR>\n" );
document.write( "d. F1(1, 1), F2(1, –5) \r<BR>\n" );
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document.write( "6. Find the slopes of the asymptotes of a hyperbola with the following equation.<BR>\n" );
document.write( "y^2/81  -  x^2/64 = 1<BR>\n" );
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document.write( "a. 8/9 <BR>\n" );
document.write( "b. 9/8 <BR>\n" );
document.write( "c. 8/9, –8/9 <BR>\n" );
document.write( "d. 9/8, –9/8 \r<BR>\n" );
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document.write( "7.Identify the type of equation presented in x2 + y2 – 4x + 12y – 6 = 0. <BR>\n" );
document.write( "a. parabola <BR>\n" );
document.write( "b. circle <BR>\n" );
document.write( "c. ellipse <BR>\n" );
document.write( "d. hyperbola \r<BR>\n" );
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document.write( "8. Solve the following system of equations.<BR>\n" );
document.write( "x2 + y2 = 64<BR>\n" );
document.write( "x2 + 64y2 = 64  \r<BR>\n" );
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document.write( "a. (8, 0), (–8, 0) <BR>\n" );
document.write( "b. (0, 8), (0, –8) <BR>\n" );
document.write( "c. (8, 0) <BR>\n" );
document.write( "d. (0, –8)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228681 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=228681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Sorry, only one question per post.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 10x\ +\ y^2\ =\ 75\">\r<BR>\n" );
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document.write( "Complete the square on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> terms.\r<BR>\n" );
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document.write( "The lead coefficient on the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> terms is 1, so simply divide the 1st degree term coefficient by 2 and square the result.  Add that result to both sides of the equation.  Since there is no 1st degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> term, there is no need to complete the square on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 10x\ +\ 25\ +\ y^2\ =\ 75\ +\ 25\">\r<BR>\n" );
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document.write( "Factor the perfect square in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in the LHS.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ 5\right)^2\ +\ y^2\ =\ 100\">\r<BR>\n" );
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document.write( "Then use the fact that the equation of a circle with center at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(h,\,k\right)\"> and radius <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ -\ h\right)^2\ +\ \left(y\ -\ k\right)^2\ =\ r^2\">\r<BR>\n" );
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document.write( "And the facts that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x\ +\ 5\right)\ =\ \left(x\ -\ (-5)\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\ =\ \left(y\ -\ 0\right)^2\">\r<BR>\n" );
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document.write( "To determine that the circle's center is at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-5,\,0\right)\"> and that the radius is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 10\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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