SOLUTION: Please help me solve this equation 9x^2+25y^2-36x+50y-164=0

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Question 1169922: Please help me solve this equation 9x^2+25y^2-36x+50y-164=0
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Write it out this way
9x^2-36x+25y^2+50y=164
9(x^2-4x)+25(y^2+2y)=164
complete the square
9(x^2-4x+4)+25(y^2+2y+1)=225, remember to multiply the 4 by 9 and the 1 by 25 and add that to the right.
9(x+2)^2+25(y+1)^2=225 Want the right side equal to 1, so divide by 225
(1/25)(x+2)^2+(1/9)(y+1)^2=1
This is an equation of an ellipse. You can also divide out the 9 and the 25 separately earlier.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B25y%5E2-36x%2B50y-164=0........group like variables and complete squares
%289x%5E2-36x%29%2B%2825y%5E2%2B50y%29-164=0
9%28x%5E2-4x%29%2B25%28y%5E2%2B2y%29-164=0
9%28x%5E2-4x%2Bb%5E2%29-9b%5E2%2B25%28y%5E2%2B2y%2Bb%5E2%29-25b%5E2-164=0
9%28x%5E2-4x%2B2%5E2%29-9%2A2%5E2%2B25%28y%5E2%2B2y%2B1%5E2%29-25%2A1%5E2-164=0
9%28x-2%29%5E2-36%2B25%28y%2B1%29%5E2-25-164=0
9%28x-2%29%5E2%2B25%28y%2B1%29%5E2-225=0.........divide by 225
9%28x-2%29%5E2%2F225%2B25%28y%2B1%29%5E2%2F225-225%2F225=0
%28x-2%29%5E2%2F25%2B%28y%2B1%29%5E2%2F9-1=0
%28x-2%29%5E2%2F25%2B%28y%2B1%29%5E2%2F9=1 ....-> ellipse, center is at (2,-1)

semimajor axis length | sqrt%2825%29=5
semiminor axis length | sqrt%289%29=3