SOLUTION: Would you please help me with a problem I don't seem to understand how to do? I need help converting this equation: {{{ -9x^2+4y^2-54x+8y-113=0 }}} into it's standard form. I have

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Would you please help me with a problem I don't seem to understand how to do? I need help converting this equation: {{{ -9x^2+4y^2-54x+8y-113=0 }}} into it's standard form. I have       Log On


   

Question 736705: Would you please help me with a problem I don't seem to understand how to do? I need help converting this equation: +-9x%5E2%2B4y%5E2-54x%2B8y-113=0+ into it's standard form. I have already figured out the general equation is a hyperbola, but can't seem to work it out.
Thanks for your help in advance.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
-9x%5E2%2B4y%5E2-54x%2B8y-113=0+
rearrange terms
-9x%5E2-54x%2B4y%5E2%2B8y-113=0+
complete the square:
-9%28x%5E2%2B6x%2B9%29%2B4%28y%5E2%2B2y%2B1%29=113-81%2B4+
-9%28x%2B3%29%5E2%2B4%28y%2B1%29%5E2=36
rearrange terms:
4%28y%2B1%29%5E2-9%28x%2B3%29%5E2=36
divide by 36
%28y%2B1%29%5E2%2F9-%28x%2B3%29%5E2%2F4=1
This is an equation of a hyperbola with vertical transverse axis:
Its standard form: %28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1, (h,k)=(x,y) coordinates of center.