document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171303>Question 1171303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> NASA is designing a new satellite to go on the international space station. The satellite disk is the shape of a parabola. The satellite will be attached to the station on a pole and will place the vertex of the satellite 4 feet away from the surface of the station. The receiver is to be positioned 7 feet above the roof. Write an equation that best models the parabolic cross section of the satellite dish.( can I see how you solve it please?) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850971 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850971\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down how to find the equation for the parabolic cross-section of the satellite dish.\r<BR>\n" );
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document.write( "**1. Set up a Coordinate System**\r<BR>\n" );
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document.write( "To make this problem easier, let's set up a coordinate system:\r<BR>\n" );
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document.write( "* Place the vertex of the parabola at the origin (0, 0).<BR>\n" );
document.write( "* Let the axis of symmetry of the parabola be the y-axis.<BR>\n" );
document.write( "* Since the receiver is above the vertex, the parabola opens upwards.\r<BR>\n" );
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document.write( "**2. Understand the Given Information**\r<BR>\n" );
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document.write( "* The vertex is 4 feet away from the surface of the station, and the receiver is 7 feet above the vertex.<BR>\n" );
document.write( "* This means the receiver is located at the point (0, 7).<BR>\n" );
document.write( "* The standard equation of a parabola that opens upwards with its vertex at the origin is:<BR>\n" );
document.write( "    * x² = 4py<BR>\n" );
document.write( "    * Where 'p' is the distance from the vertex to the focus (the location of the receiver).\r<BR>\n" );
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document.write( "**3. Find the Value of 'p'**\r<BR>\n" );
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document.write( "* In this case, the distance from the vertex (0, 0) to the receiver (focus) (0, 7) is 7 feet.<BR>\n" );
document.write( "* Therefore, p = 7.\r<BR>\n" );
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document.write( "**4. Write the Equation**\r<BR>\n" );
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document.write( "* Substitute p = 7 into the standard equation:<BR>\n" );
document.write( "    * x² = 4(7)y<BR>\n" );
document.write( "    * x² = 28y\r<BR>\n" );
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document.write( "**Therefore, the equation that best models the parabolic cross-section of the satellite dish is x² = 28y.**\r<BR>\n" );
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document.write( "**Visual Explanation**\r<BR>\n" );
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document.write( "Imagine the satellite dish in a 2D plane:\r<BR>\n" );
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document.write( "* The vertex is at (0, 0).<BR>\n" );
document.write( "* The receiver (focus) is at (0, 7).<BR>\n" );
document.write( "* The parabola opens upwards along the y-axis.\r<BR>\n" );
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document.write( "The equation x² = 28y represents this parabolic shape.<BR>\n" );
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