document.write( "Question 479772: Can you please put this equation into the standard form of a conic, step-by-step?\r
\n" ); document.write( "\n" ); document.write( "3y^2 + 20x = 23 + 5x^2 + 12y \n" ); document.write( "

Algebra.Com's Answer #328720 by ewatrrr(24785) $\"\"$ $\"About$

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document.write( "Hi,
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document.write( "putting this equation into the standard form of a conic
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document.write( "3y^2 + 20x = 23 + 5x^2 + 12y
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document.write( "3y^2 - 12y - 5x^2 + 20x = 23
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document.write( "3(y-2)^2 -12 - 5(x-2)^2 +20 = 23
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document.write( "3(y-2)^2  -5(x-2)^2 = 15
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document.write( " |Hyperbola opening up and down
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document.write( "Conics in General:
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document.write( "Standard Form of an Equation of a Circle is  
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document.write( "where Pt(h,k) is the center and r is the radius\r
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document.write( " Standard Form of an Equation of an Ellipse is 
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document.write( "where Pt(h,k) is the center and a and b  are the respective vertices distances from center.\r
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document.write( "Standard Form of an Equation of an Hyperbola opening right and  left is:
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document.write( "   where Pt(h,k) is a center  with vertices 'a' units right and left of center.
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document.write( "****Standard Form of an Equation of an Hyperbola opening up and down is:
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document.write( "   where Pt(h,k) is a center  with vertices 'b' units up and down from center.\r
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document.write( "the vertex form of a parabola opening up or down,  where(h,k) is the vertex.
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document.write( "The standard form is , where  the focus is (h,k + p)\r
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document.write( "the vertex form of a parabola opening right or left,  where(h,k) is the vertex.
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document.write( "The standard form is , where  the focus is (h +p,k )
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