SOLUTION: sketch the hyperbolic corresponding to the equation 16y^2-4x^2-36x-24y-36=0.State the centre and the equation for the asymptotes.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: sketch the hyperbolic corresponding to the equation 16y^2-4x^2-36x-24y-36=0.State the centre and the equation for the asymptotes.      Log On


   

Question 896452: sketch the hyperbolic corresponding to the equation 16y^2-4x^2-36x-24y-36=0.State the centre and the equation for the asymptotes.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
16y%5E2-4x%5E2-36x-24y-36=0
-
4y%5E2-x%5E2-9x-8y-9=0
4y%5E2-8y-x%5E2-9x=9
4%28y%5E2-2y%29-%28x%5E2%2B9x%29=0
Complete+The+Squares
4%28y%5E2-2y%2B1%29-%28x%5E2%2B9x%2B%289%2F2%29%5E2%29=9%2B4-81%2F4
4%28y-1%29%5E2-%28x%2B9%2F2%29%5E2=13-81%2F4
4%28y-1%29%5E2-%28x%2B9%2F2%29%5E2=52%2F4-81%2F4
4%28y-1%29%5E2-%28x%2B9%2F2%29%5E2=-29%2F4
-%2816%2F29%29%28y-1%29%5E2%2B%284%2F29%29%28x%2B9%2F2%29%5E2=1
highlight_green%28%28x%2B9%2F2%29%5E2%2F%2829%2F4%29-%28y-1%29%5E2%2F%2829%2F16%29=1%29

ASYMPTOTES

highlight%28y=-%28sqrt%2829%2F16%29%2Fsqrt%2829%2F4%29%29%28x%2B9%2F2%29%2B1%29
and
highlight%28y=%28sqrt%2829%2F16%29%2Fsqrt%2829%2F4%29%29%28x%2B9%2F2%29%2B1%29

These still need simplification in order to be finished.


Refer to your textbook to see how to obtain formula for the asymptotes, or refer to
other favorite reference source.