document.write( "Question 770419: 1.Find the equation of a hyperbola which has the foci of the ellipse 4x^2+9y^2=36 as vertices and the vertices of the ellipse as foci. sktch the graph.
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Algebra.Com's Answer #469517 by Edwin McCravy(20059) $\"\"$ $\"About$

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1.Find the equation of a hyperbola which has the foci of the ellipse 4x^2+9y^2=36 as vertices and the vertices of the ellipse as foci. sktch the graph.
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document.write( "4x² + 9y² = 36\r\n" );
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document.write( "Divide through by 36\r\n" );
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document.write( "That is of the form\r\n" );
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document.write( "So the ellipse has center (0,0), a=3, so the vertices are (3,0),\r\n" );
document.write( "b = 2, so covertices are (0,±2)\r\n" );
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document.write( "The distance from center to focis is c, and c² = a²-b², so we calculate c\r\n" );
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document.write( "c² = a²-b²\r\n" );
document.write( "c² = 3²-2²\r\n" );
document.write( "c² = 9-4\r\n" );
document.write( "c² = 5\r\n" );
document.write( " c = √5\r\n" );
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document.write( "Here is that ellipse:\r\n" );
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document.write( "The hyperbola has equation of the form\r\n" );
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document.write( "center (0,0), vertices (±√5,0), and foci (±3,0). To find b, we use this equation:\r\n" );
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document.write( "c² a² + b²\r\n" );
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document.write( "3² = (±√5)² + b²\r\n" );
document.write( "9 = 5 + b²\r\n" );
document.write( "4 = b²\r\n" );
document.write( "2 = b\r\n" );
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document.write( "So the hyperbola equation is\r\n" );
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document.write( "Here is the hyperbola:\r\n" );
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document.write( "2.Two members of the family of circles have radii all equal to 2 units, and are centred at (-2,2, and (2,-2)respectively.Find a member of this family that passes through the point (2,2). Sketch the graph.\r\n" );
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document.write( "If this means all the circles with radii =2, then there are an infinite number\r\n" );
document.write( "of circles with radius = 2\r\n" );
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document.write( "Choose any center which is 2 units from the point (2,2), soch as\r\n" );
document.write( " (4,2), (2,4), (0,2), (2,0).  They are the four green circles below:\r\n" );
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document.write( "The one centered at  (4,2) has equation (x-4)²+(y-2)²=4\r\n" );
document.write( "The one centered at  (2,4) has equation (x-2)²+(y-4)²=4\r\n" );
document.write( "The one centered at  (0,2) has equation x²+(y-2)²=4\r\n" );
document.write( "The one centered at  (2,0) has equation (x-2)²+y²=4\r\n" );
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document.write( "Edwin \n" );
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