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Algebra.Com's Answer #810974 by MathLover1(20850) $\"\"$ $\"About$

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$\"9x%5E2+%2B+16y%5E2+-54x+-+64y+%2B+1+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%289x%5E2-54x%29+%2B+%2816y%5E2++-+64y%29+=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x%5E2-6x%29+%2B16+%28y%5E2++-+4y%29+=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x%5E2-6x%2Bb%5E2%29+-9b%5E2%2B16+%28y%5E2++-+4y%2Bb%5E2%29+-16b%5E2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x%5E2-6x%2B3%5E2%29+-9%2A3%5E2%2B16+%28y%5E2++-+4y%2B2%5E2%29+-16%2A2%5E2=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x-3%29%5E2+-81%2B16+%28y+-+2%29%5E2+-64=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x-3%29%5E2+%2B16+%28y+-+2%29%5E2+-145=-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x-3%29%5E2+%2B16+%28y+-+2%29%5E2+=145-1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x-3%29%5E2+%2B16+%28y+-+2%29%5E2+=144\"$ ..........both sides divide by $\"144\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x-3%29%5E2%2F144+%2B16+%28y+-+2%29%5E2%2F144+=144%2F144\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-3%29%5E2%2F16+%2B+%28y+-+2%29%5E2%2F9+=1\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"h=3\"$ , $\"k=2\"$ ,
\n" ); document.write( " $\"a=sqrt%2816%29\"$ => $\"a=4\"$
\n" ); document.write( " $\"b=sqrt%289%29\"$ => $\"b=3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a%3Eb\"$ therefore $\"a\"$ is semi-major axis and $\"b\"$ is semi-minor axis \r
\n" ); document.write( "\n" ); document.write( " $\"c=sqrt%28a%5E2-b%5E2%29\"$ => $\"c=sqrt%284%5E2-3%5E2%29\"$ => $\"c=sqrt%287%29\"$ \r
\n" ); document.write( "\n" ); document.write( "1. Center: ( $\"3\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "2. Foci: ( $\"h%2Bc\"$ , $\"k\"$ ), ( $\"h-c\"$ , $\"k\"$ )\r
\n" ); document.write( "\n" ); document.write( "𝐹1 ( $\"3%2Bsqrt%287%29\"$ , $\"2\"$ ), ( $\"3-sqrt%287%29\"$ , $\"2\"$ )
\n" ); document.write( "𝐹2 ( $\"5.7\"$ , $\"2\"$ ), ( $\"-0.4\"$ , $\"2\"$ )\r
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\n" ); document.write( "\n" ); document.write( "3. Vertices: ( $\"h%2Ba\"$ , $\"k\"$ ), ( $\"h-a\"$ , $\"k\"$ )\r
\n" ); document.write( "\n" ); document.write( "𝑉1 ( $\"3%2B4\"$ , $\"2\"$ ) => ( $\"7\"$ , $\"2\"$ )
\n" ); document.write( "𝑉2 ( $\"3-4\"$ , $\"2\"$ ) => ( $\"-1\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "4. Co-vertices ( $\"h\"$ , $\"k%2Bb\"$ ), ( $\"h\"$ , $\"k-b\"$ )\r
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\n" ); document.write( "\n" ); document.write( "𝐵1 ( $\"3\"$ , $\"2%2B3\"$ ) =>( $\"3\"$ , $\"5\"$ )
\n" ); document.write( "𝐵2( $\"3\"$ , $\"2-3\"$ )=>( $\"3\"$ , $\"-1\"$ )\r
\n" ); document.write( "\n" ); document.write( "5. Endpoints of Latus Rectum\r
\n" ); document.write( "\n" ); document.write( " foci are ( $\"5.7\"$ , $\"2\"$ ), ( $\"-0.4\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "endpoints will lie on intersection of the line $\"x=5.7\"$ and the line $\"x=-0.4\"$ with ellipse\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-3%29%5E2%2F16+%2B+%28y+-+2%29%5E2%2F9+=1\"$ ...substitute $\"x\"$
\n" ); document.write( " $\"%285.7-3%29%5E2%2F16+%2B+%28y+-+2%29%5E2%2F9+=1\"$ ...solve for $\"y\"$
\n" ); document.write( " $\"0.455625%2B+%28y+-+2%29%5E2%2F9+=1\"$
\n" ); document.write( " $\"+%28y+-+2%29%5E2+=9%281-0.455625%29\"$
\n" ); document.write( " $\"+%28y+-+2%29%5E2+=4.899375\"$
\n" ); document.write( " $\"+y++=sqrt%284.899375%29%2B2\"$
\n" ); document.write( " $\"+y++=4.2\"$ or $\"+y=-0.2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-3%29%5E2%2F16+%2B+%28y+-+2%29%5E2%2F9+=1\"$ ...substitute $\"x\"$
\n" ); document.write( " $\"%28-0.4-3%29%5E2%2F16+%2B+%28y+-+2%29%5E2%2F9+=1\"$ ...solve for $\"y\"$
\n" ); document.write( " $\"0.7225%2B+%28y+-+2%29%5E2%2F9+=1\"$
\n" ); document.write( " $\"+%28y+-+2%29%5E2+=9%281-0.7225%29\"$
\n" ); document.write( " $\"+%28y+-+2%29%5E2+=2.4975\"$
\n" ); document.write( " $\"+y++=sqrt%282.4975%29%2B2\"$
\n" ); document.write( " $\"+y++=3.6\"$ or $\"+y++=0.4\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "𝐸1 ( $\"5.7\"$ , $\"4.2\"$ )
\n" ); document.write( "𝐸2 ( $\"5.7\"$ , $\"-0.2\"$ )
\n" ); document.write( "𝐸3 ( $\"-0.4\"$ , $\"3.6\"$ )
\n" ); document.write( "𝐸4 ( $\"-0.4\"$ , $\"0.4\"$ )\r
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\n" ); document.write( "\n" ); document.write( "6. Directrices:
\n" ); document.write( " $\"x=3-16sqrt%287%29%2F7\"$ =>approximately $\"x=-3.1\"$
\n" ); document.write( " $\"x=3%2B16sqrt%287%29%2F7\"$ =>approximately $\"x=9.1\"$ \r
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\n" ); document.write( "\n" ); document.write( "7. Eccentricity: $\"sqrt%287%29%2F4\"$ approximately $\"0.7\"$ \r
\n" ); document.write( "\n" ); document.write( "8. Length of LR: $\"9%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( "9. Length of Major Axis: $\"4\"$ \r
\n" ); document.write( "\n" ); document.write( "10.Length of Minor Axis: $\"3\"$ \r
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