document.write( "Question 1208374: 1. Solve the system and graph the curves: (x + 1) ^ 2 + 2 * (y - 4) ^ 2 = 12; y ^ 2 - 8y = 4x - 16 \n" ); document.write( "
Algebra.Com's Answer #846758 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The first equation can be placed in one of the standard forms of an ellipse:\r\n" );
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document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\" or \"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"\r\n" );
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document.write( "The value of \" a \" is the length of the semi-major axis and the value \" b \" is\r\n" );
document.write( "the length of the semi-minor axis.  The major axis is always longer than the\r\n" );
document.write( "minor axis.\r\n" );
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document.write( "If the number under the (x-h)2 is greater than the number under\r\n" );
document.write( "the (y-k)2, the ellipse will look like this:\"drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29\"\r\n" );
document.write( "And If the number under the (y-k)2 is greater than the number under\r\n" );
document.write( "the (x-h)2, the ellipse will look like this: \"drawing%2810%2C20%2C-1%2C1%2C-2%2C2%2Carc%280%2C0%2C1.9%2C-3.9%29+%29\"\r\n" );
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document.write( "The center is the point (h,k).\r\n" );
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document.write( "You must memorize the above, and the facts about all the conic sections if you\r\n" );
document.write( "expect to be successful doing conic section problems. You can't figure them out\r\n" );
document.write( "or look them up every time.  You won't have time on a test or exam.\r\n" );
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document.write( "\"+%28x+%2B+1%29+%5E+2+%2B+2+%2A+%28y+-+4%29+%5E+2+=+12\"\r\n" );
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document.write( "Divide through by 12 to get 1 on the right:\r\n" );
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document.write( "\"+%28x+%2B+1%29+%5E+2%2F12+%2B+2+%2A+%28y+-+4%29+%5E+2%2F12+=+12%2F12\"\r\n" );
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document.write( "\"%28x%2B1%29%5E2%2F12%2B%28y-4%29%5E2%2F6=1\"\r\n" );
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document.write( "so the center is (-1,4), the 12 is larger than the 6, so the ellipse looks\r\n" );
document.write( "like this: \"drawing%2820%2C10%2C-2%2C2%2C-1%2C1%2Carc%280%2C0%2C-3.9%2C1.9%29+%29\".\r\n" );
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document.write( "\"a%5E2=12\", so \"a=sqrt%2812%29=%223.46...%22\", \r\n" );
document.write( "\"b%5E2=6\", so \"b=sqrt%286%29=%222.449...%22\",\r\n" );
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document.write( "We plot the center (-1,4), and the major and minor axes:\r\n" );
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document.write( "Then sketch in the ellipse:\r\n" );
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document.write( "The other one is a parabola. I'll do it later if another tutor doesn't\r\n" );
document.write( "do it first.  Then we'll have to solve the system of equations and find\r\n" );
document.write( "their points of intersection, and graph both on the same set of\r\n" );
document.write( "coordinate axes.  Maybe one of the other tutors will finish.\r\n" );
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document.write( "Edwin

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