document.write( "Question 331126: Write an equation of a parabola whose vertex is at (-2,1) and focus is at (-3,1).\r
\n" ); document.write( "\n" ); document.write( "I know that h=-2 and k=1, and that there are the two formulas for a parabola with vertex (h,k):\r
\n" ); document.write( "\n" ); document.write( "horizontal: (x-h)=m(y-k)^2 and vertical: (y-k)=m(x-h)^2\r
\n" ); document.write( "\n" ); document.write( "However, I do not know which formula I am supposed to use, and why. Please help and thank you! \n" ); document.write( "

Algebra.Com's Answer #237416 by Edwin McCravy(20056) $\"\"$ $\"About$

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Write an equation of a parabola whose vertex is at (-2,1) and focus is at (-3,1).
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document.write( "We'll have to draw the parabola to determine which way it opens.\r\n" );
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document.write( "Let's draw the focus and the vertex:\r\n" );
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document.write( "The vertex and the focus are 1 unit apart. The vertex is halfway between the\r\n" );
document.write( "focus and the directrix.  Since the vertex and the focus are 1 unit apart,\r\n" );
document.write( "the directrix is the vertical line whose equation is x=-1, so we draw \r\n" );
document.write( "that directrix line in:\r\n" );
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document.write( "Now we draw a green line from the focus through the vertex to the\r\n" );
document.write( "directrix: \r\n" );
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document.write( "To help us sketch the parabola we construct two squares, \r\n" );
document.write( "one on each side of the green line from the vertex to the focus:\r\n" );
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document.write( "Now we can sketch in the parabola with the vertex and which passes\r\n" );
document.write( "through the corners of those two squares:\r\n" );
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document.write( "Remember the directrix is outside the parabola and the focus\r\n" );
document.write( "is inside the parabola.\r\n" );
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document.write( "The \"latus rectum\" or \"focal chord\" is the line across the parabola\r\n" );
document.write( "that goes through the focus and is parallel to the directrix. It's the\r\n" );
document.write( "line consisting of the left sides of the two squares.  I'll draw it in\r\n" );
document.write( "black below. Notice it is 4 units long:\r\n" );
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document.write( "The equation of the horizontal parabola which opens right or left and \r\n" );
document.write( "has vertex (h,k) is given by:\r\n" );
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document.write( "where m is the length of the \"latus rectum\" or \"focal chord\", which\r\n" );
document.write( "is the black line above, which we see is 4 units long, so m=4.\r\n" );
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document.write( "When a horizontal parabola opens right, the sign before m is +,\r\n" );
document.write( "and when a horizontal parabola opens left, the sign before the\r\n" );
document.write( "m is -, so here the sign is -.  The equation is:\r\n" );
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document.write( "That's the equation of the parabola in standard form.\r\n" );
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document.write( "Edwin

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