SOLUTION: Hi! My directions are, "Use completing the square to write the equation of each conic section in standard form. Then state the type of conic section." My first problem is...

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hi! My directions are, "Use completing the square to write the equation of each conic section in standard form. Then state the type of conic section." My first problem is...       Log On


   

Question 874248: Hi! My directions are, "Use completing the square to write the equation of each conic section in standard form. Then state the type of conic section."
My first problem is...
9x^2 - 4y^2 - 18x - 40y - 127 = 0
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2+-+4y%5E2+-+18x+-+40y+-+127+=+0

9x%5E2-18x-4y%5E2-40y-127=0
9%28x%5E2-2x%29-4%28y%5E2%2B10y%29=127
First guess is that this is a hyperbola with foci on a line parallel to the x axis.
The term to complete square for x is 1, and for y it is %2810%2F2%29%5E2=25.

9%28x%5E2-2x%2B1%29-4%28y%5E2%2B10y%2B25%29=127%2B9-100
9%28x-1%29%5E2-4%28y%2B5%29%5E2=36
highlight%28%28x-1%29%5E2%2F4-%28y%2B5%29%5E2%2F9=1%29
Hyperbola, center at (1,-5)