document.write( "Question 1181181: Dear Sir\r
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\n" ); document.write( "\n" ); document.write( "Find the general equation of the of the parabola with vertex at (5, −3) and focus at (6, −3).
\n" ); document.write( "Sketch and determine the parts of the parabola.\r
\n" ); document.write( "\n" ); document.write( "Parts of the Parabola
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\n" ); document.write( "4. Axis of Symmetry
\n" ); document.write( "5. 𝑬𝟏
\n" ); document.write( " 𝑬𝟐
\n" ); document.write( "6. Length of 𝐸1, 𝐸2\r
\n" ); document.write( "\n" ); document.write( "Thank you and God bless you.\r
\n" ); document.write( "\n" ); document.write( "Lorna \n" ); document.write( "

Algebra.Com's Answer #811054 by mccravyedwin(408) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "MathLover1 is absolutely right! I was doing \r\n" );
document.write( "some copy and pasting, and invertently \r\n" );
document.write( "copied and pasted an exponent of 2 where it\r\n" );
document.write( "should not have been.  I was lucky that the \r\n" );
document.write( "squaring was only of the number 1. Here is\r\n" );
document.write( "the entire solution corrected:\r\n" );
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document.write( "The axis of symmetry is the line through the vertex and the focus, which is\r\n" );
document.write( "the line through (5, -3) and (6, -3) is y = -3, the yellowish green line.\r\n" );
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document.write( "Since the axis of symmetry is horizontal, the equation is of the form\r\n" );
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document.write( " where (h,k) is the vertex.\r\n" );
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document.write( "So far we have (h,k) = (5,-3)\r\n" );
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document.write( "The directrix, which is always outside the parabola, is always such that the\r\n" );
document.write( "perpendicular distance from the vertex to it is the same as the distance\r\n" );
document.write( "between the vertex and the focus, this distance is |p|, and the sign of p\r\n" );
document.write( "I taken positive if the parabola opens up or right and negative if the\r\n" );
document.write( "parabola opens down or left.  This one opens right.\r\n" );
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document.write( "Since the vertex and focus are 1 unit apart, the directrix is the vertical\r\n" );
document.write( "line x = 4, the bright green line, and p=+1 so the equation is\r\n" );
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document.write( "I'm not familiar with the notation E1 and E2.  I'm guessing that E1 and E2\r\n" );
document.write( "are the ends of the latus rectum, or focal chord, the vertical line segment\r\n" );
document.write( "that goes through the focus, the blue line segment.  Its length is the same\r\n" );
document.write( "as 4p.\r\n" );
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document.write( "So we plug x = 6 in the equation and solve for y:\r\n" );
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document.write( "Using the \"+\", y+3 = 2, y = -1, so E1 = (6,-1)\r\n" );
document.write( "Using the \"-\", y+3 = -2, y = -5, so E2 = (6,-5)\r\n" );
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document.write( "We find that its length is 4, which is the same as 4p.\r\n" );
document.write( "If I guessed wrong about E1 and E2, tell me how your \r\n" );
document.write( "book or teacher defines them in the thank-you note\r\n" );
document.write( "at the bottom of this page and I'll get back to you\r\n" );
document.write( "by email. \r\n" );
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document.write( "Edwin \n" );
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