document.write( "Question 1181166: Dear Sir,\r
\n" ); document.write( "\n" ); document.write( "Please help me solve this problem and please show me your solution.\r
\n" ); document.write( "\n" ); document.write( "Given by the equation 49𝑥2 + 9𝑦2 = 441, sketch and determine the parts of an ellipse.\r
\n" ); document.write( "\n" ); document.write( "Solve for the value a, b, c\r
\n" ); document.write( "\n" ); document.write( "Parts of an Ellipse\r
\n" ); document.write( "\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 Rectum
\n" ); document.write( "𝐸1
\n" ); document.write( "𝐸2
\n" ); document.write( "𝐸3
\n" ); document.write( "𝐸4
\n" ); document.write( "6. Directrices\r
\n" ); document.write( "\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. More Power.\r
\n" ); document.write( "\n" ); document.write( "Sincerely yours,\r
\n" ); document.write( "\n" ); document.write( "Lorna
\n" ); document.write( "

Algebra.Com's Answer #811026 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
Given by the equation \r
\n" ); document.write( "\n" ); document.write( "\"49x%5E2+%2B+9y%5E2+=+441\"........both sides divide by \"441\"\r
\n" ); document.write( "\n" ); document.write( "\"49x%5E2%2F441+%2B+9y%5E2%2F441+=+441%2F441\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2F9+%2B+y%5E2%2F49+=+1\"\r
\n" ); document.write( "\n" ); document.write( "=>center is at origin, \"h=0\",\"k=0\"
\n" ); document.write( "=>\"a=sqrt%289%29=3\"
\n" ); document.write( "=>\"b=sqrt%2849%29=7\"\r
\n" ); document.write( "\n" ); document.write( "\"b%3Ea\"=> you have vertical ellipse\r
\n" ); document.write( "\n" ); document.write( "\"c=sqrt%28b%5E2-a%5E2%29\"
\n" ); document.write( "\"c=sqrt%2849-9%29\"
\n" ); document.write( "\"c=sqrt%2840%29\"
\n" ); document.write( "\"c=sqrt%284%2A10%29\"
\n" ); document.write( "\"c=2sqrt%2810%29\"\r
\n" ); document.write( "\n" ); document.write( "1. Center
\n" ); document.write( "2. Foci: (\"h\",\"c\"),(\"h\",\"-c\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "𝐹1 (\"0\", \"2sqrt%2810%29\")
\n" ); document.write( "𝐹2 (\"0\", \"-2sqrt%2810%29\")\r
\n" ); document.write( "\n" ); document.write( "3. Vertices: (\"h\",\"b\"),(\"h\",\"-b\")
\n" ); document.write( "𝑉1 (\"0\",\"7\")
\n" ); document.write( "𝑉2 (\"0\",\"-7\")\r
\n" ); document.write( "\n" ); document.write( "4. Co-vertices:(\"a\",\"k\"),(\"-a\",\"k\")
\n" ); document.write( "𝐵1 (\"3\",\"0\")
\n" ); document.write( "𝐵2 (\"-3\",\"0\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "5. Endpoints of Latus Rectum\r
\n" ); document.write( "\n" ); document.write( "use the coordinate of the focus \"y=2sqrt%2810%29\", substitute in ellipe equation and solve for \"x\"
\n" ); document.write( "\"x%5E2%2F9+%2B+%282sqrt%2810%29%29%5E2%2F49+=+1\"
\n" ); document.write( "\"x%5E2%2F9+%2B+40%2F49+=+1\"
\n" ); document.write( "\"x%5E2%2F9+++=+1-40%2F49\"
\n" ); document.write( "\"x%5E2%2F9+++=+9%2F49\"
\n" ); document.write( "\"x%5E2++=+9%289%2F49%29\"...simplify
\n" ); document.write( "\"x%5E2++=+9%2F7\"\r
\n" ); document.write( "\n" ); document.write( "\"x=+sqrt%289%2F7%29\"
\n" ); document.write( "\"x=+3%2Fsqrt%287%29\"
\n" ); document.write( "\"x=+3sqrt%287%29%2F7\" or \"x=+-3sqrt%287%29%2F7\"\r
\n" ); document.write( "\n" ); document.write( ",\r
\n" ); document.write( "\n" ); document.write( "𝐸1(\"3sqrt%287%29%2F7\",\"2sqrt%2810%29\")
\n" ); document.write( "𝐸2(\"-3sqrt%287%29%2F7\",\"2sqrt%2810%29\")
\n" ); document.write( "𝐸3(\"3sqrt%287%29%2F7\",\"-2sqrt%2810%29\")
\n" ); document.write( "𝐸4(\"-3sqrt%287%29%2F7\",\"-2sqrt%2810%29\")\r
\n" ); document.write( "\n" ); document.write( "6. Directrices: \"y=49sqrt%2810%29%2F20\" , \"y=-49sqrt%2810%29%2F20\"
\n" ); document.write( "7. Eccentricity:\"2sqrt%2810%29%2F7\"
\n" ); document.write( "8. Length of LR:\"18%2F7\"
\n" ); document.write( "9. Length of Major Axis:\"14\"
\n" ); document.write( "10.Length of Minor Axis:\"6\"\r
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\n" ); document.write( "\n" ); document.write( " \r
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