How do you write a standard form equation for the hyperbola with #9x^2-100y^2+18x+600y+9=0#?

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Answer 1 · 2015-11-17T18:37:59

Simply complete the square for both the x and y variables.

First, group together by variable and simplify:

#9(x^2+2x)-100(y^2-6y)=-9#

Next, complete the squares, but be sure to keep both sides of the equation balanced!

#9(x^2+2x)-100(y^2-6y)=-9#

#9(x^2+2x+1)-100(y^2-6y+9)=-9+9-900#

#9(x+1)^2-100(y-3)^2=-900#

Finally, divide by -900

#(y-3)^2/9-(x+1)^2/100=1#

So, this is a hyperbola with center #C=(-1,3)#

hope that helped

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