SOLUTION: Dear Sir, Please help me solve this problem with your solution. Convert the general equation 25x2-16y2+250x+32y+109=0 Thank you very much and God bless you. Sincerely y

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Dear Sir, Please help me solve this problem with your solution. Convert the general equation 25x2-16y2+250x+32y+109=0 Thank you very much and God bless you. Sincerely y      Log On


   

Question 1181118: Dear Sir,
Please help me solve this problem with your solution.
Convert the general equation 25x2-16y2+250x+32y+109=0
Thank you very much and God bless you.
Sincerely yours,
Lorna
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite as 25x^2+250x-16y^2+32y=-109
This is 25 (x^2+10x)-16(y^2-2y)=-109
or 25 (x^2+10x+25)-16(y^2-2y+1)=-109 +625-16, completing the square
or 25(x+5)^2-16(y-1)^2=500
divide now by 500 to make the right side 1
(x+5)^2/20-(y-1)^2/(500/16)=1
a^2=20, a=+/-2 sqrt(5)
b^2=500/16, b=+/-(5/2)sqrt(5)