Question 204874This question is from textbook College Algebra
: Identify the center, vertices and foci x^2-10x-2y+19=0
This question is from textbook College Algebra
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! x^2 -10x =2y-19
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complete square,,,(10/2)^2 =25
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x^2 -10x +25 = 2y -19 +25,,,,,,,add 25 to both sides
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(x-5)^2 = 2y +6 = 2(y+3)
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(1/2) (x-5)^2 = (y+3),,,,form is A(x-h)^2 = (y-k)
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vertex is at (h,k) ,,,,or,,,(5,-3)
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curve is an y parabola,,,opening up
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focus is at (o,p) where p is found from x^2 =4p y
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(x^2) = 2(y),,,,,or 4p = 2,,,p=1/2
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That is focus is 1/2 above center,,,or,,,(5, -2.5)
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x intercepts are at y=0,,,,,1/2(x-5)^2 =(0+3),,,(x-5)^2 =6,,(x-5)=sqrt6,
(x-5) = +/- 2.449,,,,x= 2.449,,,7.449
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directrix is at (p) below vertex,,,or (y= -3.5)
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