SOLUTION: What conic does the equation x2 - 5x + 10y + 11 = 0 represent? please please help! A. parabola B. hyperbola C. circle D. ellipse which could it be?

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: What conic does the equation x2 - 5x + 10y + 11 = 0 represent? please please help! A. parabola B. hyperbola C. circle D. ellipse which could it be?      Log On


   

Question 288666: What conic does the equation x2 - 5x + 10y + 11 = 0 represent? please please help! A. parabola
B. hyperbola
C. circle
D. ellipse
which could it be?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+5x+%2B+10y+%2B+11+=+0 Start with the given equation.


x%5E2+-+5x+%2B+10y++=+-11 Subtract 11 from both sides.


x%5E2+%2B+10y++=+-11%2B5x Add 5x to both sides


10y++=+-11%2B5x-x%5E2 Subtract x%5E2 from both sides


10y++=+-x%5E2%2B5x-11 Rearrange the terms into descending degree.


y++=+%28-x%5E2%2B5x-11%29%2F10 Divide both sides by 10 to isolate 'y'.


y++=+%28-x%5E2%29%2F10%2B%285x%29%2F10-11%2F10 Break up the fraction.


y++=+-%281%2F10%29x%5E2%2B%281%2F2%29x-11%2F10 Reduce and simplify.


Now that y++=+-%281%2F10%29x%5E2%2B%281%2F2%29x-11%2F10 is in the form y=ax%5E2%2Bbx%2Bc, which is the general equation for a parabola, this means that y++=+-%281%2F10%29x%5E2%2B%281%2F2%29x-11%2F10 is a parabola where a=-1%2F10, b=1%2F2 and c=-11%2F10


Because y++=+-%281%2F10%29x%5E2%2B%281%2F2%29x-11%2F10 is equivalent to x%5E2+-+5x+%2B+10y+%2B+11+=+0, x%5E2+-+5x+%2B+10y+%2B+11+=+0 is also a parabola.


So x%5E2+-+5x+%2B+10y+%2B+11+=+0 is a parabola.