document.write( "Question 715834: Identify the conic, write its equation in standard form, and give the vertex/vertices and focus/foci.\r
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Algebra.Com's Answer #439660 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "x² + 4x - 8y + 36 = 0\r\n" );
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document.write( "Since the x is the variable that is squared, get all terms\r\n" );
document.write( "in x on the left and other terms on the right:\r\n" );
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document.write( "          x² + 4x = 8y - 36\r\n" );
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document.write( "Complete the square on the left \r\n" );
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document.write( "1. Multiply the coefficient of x, which is 4, by , getting 2\r\n" );
document.write( "2. Square that result, getting 4\r\n" );
document.write( "3.  Add to both sides.\r\n" );
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document.write( "      x² + 4x + 4 = 8y - 36 + 4\r\n" );
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document.write( "Factor the left side, collect like terms on the right\r\n" );
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document.write( "   (x + 2)(x + 2) = 8y - 32\r\n" );
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document.write( "Write the left side as a perfect square.  Factor 8 out on the right\r\n" );
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document.write( "         (x + 2)² = 8(y - 4)\r\n" );
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document.write( "Compare to\r\n" );
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document.write( "         (x - h)² = 4p(y - k)\r\n" );
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document.write( "with vertex (h,k) = (-2,4)  4p = 8, so p = 2\r\n" );
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document.write( "We plot the vertex\r\n" );
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document.write( "Since p is positive, the parabola opens upward. the directrix\r\n" );
document.write( "is p=2 units below the vertex and has the equation y = k-p or\r\n" );
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document.write( "y = 4-2 or y=2\r\n" );
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document.write( "It is the green line below\r\n" );
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document.write( "The focus is p=2 units above the vertex (h,k+p) or (-2,4+2) or (2,6) \r\n" );
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document.write( "Draw a line from the focus directly to the directrix and draw 2\r\n" );
document.write( "squares on each side of that line, like this.\r\n" );
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document.write( "Then sketch in the parabola through the vertex and the upper outer\r\n" );
document.write( "corners of the two squares:\r\n" );
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document.write( "Edwin

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