document.write( "Question 204874This question is from textbook College Algebra
\n" ); document.write( ": Identify the center, vertices and foci x^2-10x-2y+19=0 \n" ); document.write( "
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x^2 -10x =2y-19
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\n" ); document.write( "complete square,,,(10/2)^2 =25
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\n" ); document.write( "x^2 -10x +25 = 2y -19 +25,,,,,,,add 25 to both sides
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\n" ); document.write( "(x-5)^2 = 2y +6 = 2(y+3)
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\n" ); document.write( "(1/2) (x-5)^2 = (y+3),,,,form is A(x-h)^2 = (y-k)
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\n" ); document.write( "vertex is at (h,k) ,,,,or,,,(5,-3)
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\n" ); document.write( "curve is an y parabola,,,opening up
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\n" ); document.write( "focus is at (o,p) where p is found from x^2 =4p y
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\n" ); document.write( "(x^2) = 2(y),,,,,or 4p = 2,,,p=1/2
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\n" ); document.write( "That is focus is 1/2 above center,,,or,,,(5, -2.5)
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\n" ); document.write( "x intercepts are at y=0,,,,,1/2(x-5)^2 =(0+3),,,(x-5)^2 =6,,(x-5)=sqrt6,
\n" ); document.write( "(x-5) = +/- 2.449,,,,x= 2.449,,,7.449
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\n" ); document.write( "directrix is at (p) below vertex,,,or (y= -3.5)
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