\r\n" );
document.write( "Classify the conic section:\r\n" );
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document.write( "1. x² + y² = 36 <-- circle since x² and y² have the SAME COEFFICIENT, 1,\r\n" );
document.write( " when on the same side of the equation. \r\n" );
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document.write( "2. x² - y² = 36 <-- hyperbola since x² and y² have coefficients with\r\n" );
document.write( " OPPOSITE SIGNS when on the same side of the equation.\r\n" );
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document.write( "3. 5x² + 9y² = 45 <-- ellipse since x² and y² have different coefficients \r\n" );
document.write( " with THE SAME SIGN when on the same side of the \r\n" );
document.write( " equation.\r\n" );
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document.write( " 4. x² + y² = 121 <-- circle since x² and y² have the SAME COEFFICIENT, 1,\r\n" );
document.write( " when on the same side of the equation. \r\n" );
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document.write( " 5. y = 17 <-- line because it has NO x² or y² terms.\r\n" );
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document.write( "6. What is the standard equation of the circle with radius 4, and center (0,0)?\r\n" );
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document.write( "Start woth \r\n" );
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document.write( " (x-h)²+(y-k)²=r² where (h,k) is the center and r is the radius\r\n" );
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document.write( " (x-0)²+(y-0)²=4²\r\n" );
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document.write( " x² + y² = 16\r\n" );
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document.write( "7. What is the standard equation of the circle with radius 5, and center (-5,-1)?\r\n" );
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document.write( "Start woth \r\n" );
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document.write( " (x-h)²+(y-k)²=r² where (h,k) is the center and r is the radius\r\n" );
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document.write( " (x-(-5))²+(y-(-1))²=5²\r\n" );
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document.write( " (x+5)² + (y+1)² = 25\r\n" );
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document.write( "8. Name the center and radius of the circle whose equation is x² + y² = 49.\r\n" );
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document.write( " The reverse of the other problems:\r\n" );
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document.write( " Write it as\r\n" );
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document.write( " (x-0)²+(y-0)²=7²\r\n" );
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document.write( " Compare that to\r\n" );
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document.write( " (x-h)²+(y-k)²=r²\r\n" );
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document.write( " So the center is (h,k) = (0,0,) and its radius is 7 \r\n" );
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document.write( "9. What are the vertices of the ellipse whose equation is (x²)/25 + (y²)/9 = 1?\r\n" );
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document.write( " The ellipse that has equation \r\n" );
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document.write( " 
\r\n" );
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document.write( " Since a > b, and a is uder x, the ellipse looks like this 
\r\n" );
document.write( "\r\n" );
document.write( " has vertices (h+a,k) and (h-a,k). The center is (h,k)\r\n" );
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document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Then the vertices are (h+a,k) and (h-a,k) which are\r\n" );
document.write( " (0+5,0) and (0-5,0)\r\n" );
document.write( " (5,0) and (-5,0)\r\n" );
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document.write( "10. What are the vertices of the ellipse whose equation is (x²)/9 + (y²)/36 = 1?\r\n" );
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document.write( " The ellipse that has equation \r\n" );
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document.write( " 
\r\n" );
document.write( "\r\n" );
document.write( " Since a > b, and a is under y, the ellipse looks like this 
\r\n" );
document.write( " \r\n" );
document.write( "has vertices (h,k+a) and (h,k-a). The center is (h,k)\r\n" );
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document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Then the vertices are (h,k+a) and (h,k-a) which are\r\n" );
document.write( " (0,0+6) and (0,0-6)\r\n" );
document.write( " (0,-6) and (0,6)\r\n" );
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document.write( "11. What is the center of the ellipse whose equation is (x²)/25 + (y²)/4 = 1?\r\n" );
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document.write( " Write it as\r\n" );
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document.write( " 
\r\n" );
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document.write( " compare to\r\n" );
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document.write( " \r\n" );
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document.write( " So center = (h,k) = (0,0) \r\n" );
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document.write( "12. What is the center of the ellipse whose equation is (x+1)²/4 + (y²)/1 = 1?\r\n" );
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document.write( " \r\n" );
document.write( " The ellipse that has equation \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " Since a > b, and a is under x, the ellipse looks like this \r\n" );
document.write( "\r\n" );
document.write( " It has center is (h,k)\r\n" );
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document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Compare it to\r\n" );
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document.write( " \r\n" );
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document.write( " and see x+1 = x-h and y-k = y-0\r\n" );
document.write( " 1 = -h -k = 0\r\n" );
document.write( " -1 = h k = 0\r\n" );
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document.write( " So the center = (h,k) = (-1,0)\r\n" );
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document.write( "13. What is the center of the hyperbola whose equation is (x²) - (y²) = 1?\r\n" );
document.write( "\r\n" );
document.write( " The hyperbola that has equation \r\n" );
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document.write( " 
\r\n" );
document.write( "\r\n" );
document.write( " Since a is uder x, the hyperbola looks like this )(\r\n" );
document.write( "\r\n" );
document.write( " It has has center is (h,k)\r\n" );
document.write( "\r\n" );
document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Compare to\r\n" );
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document.write( " 
\r\n" );
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document.write( " and h=0, k=0, so its center is (h,k) = (0,0) \r\n" );
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document.write( "14. What is the center of the hyperbola whose equation is (x²)/4 - (y²)/9 = 1?\r\n" );
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document.write( " The hyperbola that has equation \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " Since a is uder x, the hyperbola looks like this )(\r\n" );
document.write( " It has has center is (h,k)\r\n" );
document.write( "\r\n" );
document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Compare to\r\n" );
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document.write( " \r\n" );
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document.write( " and h=0, k=0, so its center is (h,k) = (0,0)\r\n" );
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document.write( "15. What is the center of the hyperbola whose equation is [(x+2)²/9] - [(y-2)²/16] = 1?\r\n" );
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document.write( " The hyperbola that has equation \r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " Since a is under x, the hyperbola looks like this )(\r\n" );
document.write( " It has has center is (h,k)\r\n" );
document.write( "\r\n" );
document.write( " Write your equation as\r\n" );
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document.write( " 
\r\n" );
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document.write( " Compare to\r\n" );
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document.write( " \r\n" );
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document.write( " x-h = x+2 y-k = y-2\r\n" );
document.write( " -h = 2 -k = -2\r\n" );
document.write( " h = -2 k = 2\r\n" );
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document.write( " So the center is (h,k) = (-2,2)\r\n" );
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document.write( " 16. How does the graph of the hyperbola whose equation is (x²)/9 - (y²)/25 = 1 open?\r\n" );
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document.write( " The hyperbola that has equation \r\n" );
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document.write( " \r\n" );
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document.write( " Since a is under x, the hyperbola looks like this )(,\r\n" );
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document.write( " so it opens right and left\r\n" );
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document.write( "17. How does the graph of the hyperbola whose equation is (y²)/4 - (x²)/9 = 1\r\n" );
document.write( " open?\r\n" );
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document.write( " The hyperbola that has equation \r\n" );
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document.write( " \r\n" );
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document.write( " Since a is under y, the hyperbola looks like this 
\r\n" );
document.write( " so it opens up and down.\r\n" );
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document.write( " 18. Classify the conic section of the equation x² + 2x + y² + 6y = 15.\r\n" );
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document.write( "Circle since x² and y² have the SAME COEFFICIENT, 1, when on the same \r\n" );
document.write( "side of the equation.\r\n" );
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document.write( " 19. Classify the conic section of the equation 4x² + 9y² - 8x - 18y - 19 = 0.\r\n" );
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document.write( "Ellipse since x² and y² have different coefficients with THE SAME SIGNS when\r\n" );
document.write( "on the same side of the equation.\r\n" );
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document.write( "20. Classify the conic section of the equation 9x² - 3 = 18x + 4y.\r\n" );
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document.write( "Parabola since there is only one term that has a variable squared.\r\n" );
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document.write( "Edwin
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