document.write( "Question 1092594: Find an equation of an ellipse having a vertex at (3,7) and foci at (3,-1) and (3,5). \n" ); document.write( "

Algebra.Com's Answer #707294 by ikleyn(52802) $\"\"$ $\"About$

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document.write( "1.  Notice that the foci are located on the line x = 3 (they have equal x-coordinates).\r\n" );
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document.write( "    Therefore, the major axis is the vertical line x = 3.\r\n" );
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document.write( "2.  The center of the ellipse is the midpoint between the foci, i.e. (3,2).\r\n" );
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document.write( "3.  The distance between the foci is 3 - (-3) = 6 units.\r\n" );
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document.write( "    Hence, the linear eccentricity of the ellipse is half of that, i.e. e= 6/2 = 3.\r\n" );
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document.write( "4.  The given point (3,7) lies on the same line x= 3 (on the major line), hence, it is a vertex.\r\n" );
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document.write( "    Then the major semi-axis length is the distance from the center to the vertex, i.e. a= 5 units.\r\n" );
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document.write( "5.  For the minor semi-axis,  we have an expression  b =  =  = 4.\r\n" );
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document.write( "6.  Thus, the center of the ellipse is  (3,2), the major semi-axis is a= 5 units, and the minor semi-axis is 4 units.\r\n" );
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document.write( "    Now we can write the standard equation of the ellipse\r\n" );
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document.write( "     +  = 1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ellipse definition, canonical equation, characteristic points and elements \r
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\n" ); document.write( "\n" ); document.write( "    - Standard equation of an ellipse\r
\n" ); document.write( "\n" ); document.write( "    - Find the standard equation of an ellipse given by its elements\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Ellipses. Definition, major elements and properties. Solved problems\".\r
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