document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119425>Question 1119425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the standard equation of an ellipse with the first focus being (-4,0) and the second one being (4,0), passing through (4,1) </SPAN>\n" );
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document.write( "With foci at (-4,0) and (4,0), the center of the ellipse is at (0,0).  The equation is of the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The distance from the center of the ellipse to each focus is c, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2+=+a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"c%5E2+=+a%5E2-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since that distance is 4, we have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-b%5E2+=+c%5E2+=+16 ALIGN=MIDDLE  ALT=\"a%5E2-b%5E2+=+c%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+b%5E2%2B16 ALIGN=MIDDLE  ALT=\"a%5E2+=+b%5E2%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the equation of the ellipse can be written as<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28b%5E2%2B16%29+%2B+y%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%28b%5E2%2B16%29+%2B+y%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We can find the value of b^2 by plugging in the coordinates of the known point on the ellipse, (4,1).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F%28b%5E2%2B16%29%2B1%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"16%2F%28b%5E2%2B16%29%2B1%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%28b%5E2%29%2B%28b%5E2%2B16%29+=+b%5E2%28b%5E2%2B16%29 ALIGN=MIDDLE  ALT=\"16%28b%5E2%29%2B%28b%5E2%2B16%29+=+b%5E2%28b%5E2%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17b%5E2%2B16+=+b%5E4%2B16b%5E2 ALIGN=MIDDLE  ALT=\"17b%5E2%2B16+=+b%5E4%2B16b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E4-b%5E2-16+=+0 ALIGN=MIDDLE  ALT=\"b%5E4-b%5E2-16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+=+%281%2Bsqrt%2865%29%29%2F2 ALIGN=MIDDLE  ALT=\"b%5E2+=+%281%2Bsqrt%2865%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+=+b%5E2%2B16+=+%281%2Bsqrt%2865%29%29%2F2%2B16+=+%2833%2Bsqrt%2865%29%29%2F2 ALIGN=MIDDLE  ALT=\"a%5E2+=+b%5E2%2B16+=+%281%2Bsqrt%2865%29%29%2F2%2B16+=+%2833%2Bsqrt%2865%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "And finally the equation is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28%2833%2Bsqrt%2865%29%29%2F2%29%2By%5E2%2F%28%281%2Bsqrt%2865%29%29%2F2%29+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%28%2833%2Bsqrt%2865%29%29%2F2%29%2By%5E2%2F%28%281%2Bsqrt%2865%29%29%2F2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );