SOLUTION: convert the general equation 16x2+25y2-160x-200y+400=0 to standard form

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: convert the general equation 16x2+25y2-160x-200y+400=0 to standard form      Log On


   

Question 1180973: convert the general equation 16x2+25y2-160x-200y+400=0 to standard form
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

16x%5E2%2B25y%5E2-160x-200y%2B400=0
to convert the general equation to standard form, complete squares
%2816x%5E2-160x%29%2B%2825y%5E2-200y%29%2B400=0

16%28x%5E2-10x%29%2B25%28y%5E2-8y%29%2B400=0

16%28x%5E2-10x%2Bb%5E2%29-16b%5E2%2B25%28y%5E2-8y%2Bb%5E2%29-25b%5E2%2B400=0...for x part b=10%2F2=5, and for y part b=8%2F2=4

16%28x%5E2-10x%2B5%5E2%29-16%2A5%5E2%2B25%28y%5E2-8y%2B4%5E2%29-25%2A4%5E2%2B400=0

16%28x-5%29%5E2-400%2B25%28y-4%29%5E2-400%2B400=0

16%28x-5%29%5E2%2B25%28y-4%29%5E2=400.........both sides divide by 400

16%28x-5%29%5E2%2F400%2B25%28y-4%29%5E2%2F400=400%2F400

%28x-5%29%5E2%2F25%2B%28y-4%29%5E2%2F16=1