SOLUTION: i dont know how to solve this problem so that i get the equation of an ellipse 4x^2+9y^2+16x-18y-11=0

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Question 134309This question is from textbook Merill algebra 2
: i dont know how to solve this problem so that i get the equation of an ellipse
4x^2+9y^2+16x-18y-11=0 This question is from textbook Merill algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B9y%5E2%2B16x-18y-11=0 Start with the given equation


4x%5E2%2B16x%2B9y%5E2-18y-11=0 Rearrange the terms


4x%5E2%2B16x%2B9y%5E2-18y=%2B11 Add 11 to both sides


4%28x%2B2%29%5E2-16%2B9y%5E2-18y=%2B11 Complete the square for the x terms


4%28x%2B2%29%5E2-16%2B9%28y-1%29%5E2-9=%2B11 Complete the square for the y terms


4%28x%2B2%29%5E2%2B9%28y-1%29%5E2-25=%2B11 Combine like terms


4%28x%2B2%29%5E2%2B9%28y-1%29%5E2=%2B11%2B25 Add 25 to both sides


4%28x%2B2%29%5E2%2B9%28y-1%29%5E2=36 Combine like terms




%284%28x%2B2%29%5E2%2B9%28y-1%29%5E2%29%2F%2836%29=cross%28%2836%29%2F%2836%29%29Now divide both sides by 36 to make the right side equal to 1



%284%28x%2B2%29%5E2%29%2F%2836%29%2B%289%28y-1%29%5E2%29%2F%2836%29=1 Simplify and break up the fraction


%28%28x%2B2%29%5E2%29%2F%289%29%2B%28%28y-1%29%5E2%29%2F%284%29=1 Reduce


Notice how the equation is now in the form %28x-h%29%5E2%2F%28a%5E2%29%2B%28y-k%29%5E2%2F%28b%5E2%29=1. This means that this conic section is an ellipse.