document.write( "Question 1181121: Dear Sir,\r
\n" ); document.write( "\n" ); document.write( "Please help me solve this problem and please show your solution also because am really very slow in Math am already 61 years old.\r
\n" ); document.write( "\n" ); document.write( "Find the equation of the ellipse with center at (0, 0), length of major axis is 8, and a focus at (0, −2). Identify the parts of the ellipse and sketch the graph.\r
\n" ); document.write( "\n" ); document.write( "Parts of an Ellipse Graph of an Ellipse
\n" ); document.write( "1. Center
\n" ); document.write( "2. Foci
\n" ); document.write( "𝐹1
\n" ); document.write( "𝐹2
\n" ); document.write( "3. Vertices
\n" ); document.write( "𝑉1
\n" ); document.write( "𝑉2
\n" ); document.write( "4. Co-vertices
\n" ); document.write( "𝐵1
\n" ); document.write( "𝐵2
\n" ); document.write( "5. Endpoints of Latus
\n" ); document.write( "Rectum
\n" ); document.write( "𝐸1
\n" ); document.write( "𝐸2
\n" ); document.write( "𝐸3
\n" ); document.write( "𝐸4
\n" ); document.write( "6. Directrices
\n" ); document.write( "7. Eccentricity
\n" ); document.write( "8. Length of LR
\n" ); document.write( "9. Length of Major Axis
\n" ); document.write( "10.Length of Minor Axis\r
\n" ); document.write( "\n" ); document.write( "Thank you very much and God Bless you.\r
\n" ); document.write( "\n" ); document.write( "Lorna\r
\n" ); document.write( "\n" ); document.write( "
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Algebra.Com's Answer #810957 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
Find the equation of the ellipse \r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"\r
\n" ); document.write( "\n" ); document.write( "with center at (\"0\", \"0\"), =>\"h=0\",\"k=0\"\r
\n" ); document.write( "\n" ); document.write( "the equation of the ellipse is\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1\"\r
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\n" ); document.write( "\n" ); document.write( "length of major axis is \"2a=8\"=>\"a=4\" \r
\n" ); document.write( "\n" ); document.write( "and a focus at (\"0\", \"-2\")\r
\n" ); document.write( "\n" ); document.write( "since a focus is at (\"0\", \"c\")=>\"c=2\"
\n" ); document.write( " and
\n" ); document.write( "other focus is on oposite side of the center at (\"0\", \"2\")\r
\n" ); document.write( "\n" ); document.write( "\"b%5E2=a%5E2-c%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"b%5E2=4%5E2-%28-2%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"b%5E2=16-4\"\r
\n" ); document.write( "\n" ); document.write( "\"b%5E2=12\"\r
\n" ); document.write( "\n" ); document.write( "\"b=sqrt%2812%29\"\r
\n" ); document.write( "\n" ); document.write( "\"b=sqrt%284%2A3%29\"\r
\n" ); document.write( "\n" ); document.write( "\"b=2sqrt%283%29\"\r
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\n" ); document.write( "\n" ); document.write( "your equation is: major axis is on y-axis, so \"a\" goes with \"y\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\"
\n" ); document.write( "\"x%5E2%2F12%2By%5E2%2F16=1\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1. Center (\"0\", \"0\")
\n" ); document.write( "2. Foci
\n" ); document.write( "𝐹1 (\"0\", \"-2\")
\n" ); document.write( "𝐹2(\"0\", \"2\")\r
\n" ); document.write( "\n" ); document.write( "3. Vertices V =>(\"0\",\"a\"),(\"0\",\"-a\")
\n" ); document.write( "𝑉1 (\"0\",\"-4\")
\n" ); document.write( "𝑉2(\"0\",\"4\")\r
\n" ); document.write( "\n" ); document.write( "4. Co-vertices =>(\"b\",\"0\"),(\"-b\",\"0\")
\n" ); document.write( "𝐵1(\"2sqrt%283%29\", \"0\")
\n" ); document.write( "𝐵2(\"-2sqrt%283%29\", \"0\")\r
\n" ); document.write( "\n" ); document.write( "5. Endpoints of Latus
\n" ); document.write( "Rectum
\n" ); document.write( "𝐸1 (\"h-b%5E2%2Fa\", \"k%2Bc\")=> (\"0-12%2F4\", \"0%2B2\")=> (\"-3\", \"2\")
\n" ); document.write( "𝐸2(\"h%2Bb%5E2%2Fa\", \"k%2Bc\")=> (\"0%2B12%2F4\", \"0%2B2\")=> (\"3\", \"2\")
\n" ); document.write( "𝐸3(\"h-b%5E2%2Fa\", \"k-c\")=> (\"0-12%2F4\", \"0-2\")=> (\"-3\", \"-2\")
\n" ); document.write( "𝐸4(\"h%2Bb%5E2%2Fa\", \"k-c\")=> (\"0%2B12%2F4\", \"0-2\")=> (\"3\", \"-2\")\r
\n" ); document.write( "\n" ); document.write( "6. Directrices: \"y=-8\", \"y=8\"\r
\n" ); document.write( "\n" ); document.write( "7. Eccentricity:\"1%2F2\"\r
\n" ); document.write( "\n" ); document.write( "8. Length of LR:\"6\"
\n" ); document.write( "First latus rectum: \"y=-2\"
\n" ); document.write( "Second latus rectum:\"y=2\"
\n" ); document.write( "The length of the latera recta: \"6\"\r
\n" ); document.write( "\n" ); document.write( "9. Length of Major Axis:\"8\"
\n" ); document.write( "10.Length of Minor Axis:\"4\"\r
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