SOLUTION: Classify the conic represented by the equation 5y^2+6x-11=5x^2+6y+25. My assumption is the conic represents a hyperbola because both of the terms are squared, however, I do not

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Classify the conic represented by the equation 5y^2+6x-11=5x^2+6y+25. My assumption is the conic represents a hyperbola because both of the terms are squared, however, I do not       Log On


   

Question 716534: Classify the conic represented by the equation 5y^2+6x-11=5x^2+6y+25.
My assumption is the conic represents a hyperbola because both of the terms are squared, however, I do not understand how to put this equation into standard form.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Let me be brief, and maybe you could discuss this if it is still a difficulty for you:
The last step would be to compare the form of the resulting equation to the general models for the conic section equations. The first step should or could be to Complete the Square for the x and the y terms. Then simplify and put into a standard form for whichever conic section the equation will represent.

What to do: Complete the Square for the x terms and for the y terms, simplify, put into whichever standard form fits. Compare with the known conic section equation model forms.

MORE: The term to add and subtract was %283%2F5%29%5E2, in order to Complete the Square.

Skipping all the steps and algebra and simplifications, since text typing here is long I just give the resulting equation:

Not necessarily the best form, but
%28y-3%2F5%29%5E2%2F%2836%2F5%29-%28x-3%2F5%29%5E2%2F%2836%2F5%29=1
Appears to be hyperbola.

Do you really want all of the steps? I skipped them here. Pencil and paper was less trouble by far.