SOLUTION: Find the vertices and foci of the conic. 25x^2 + 4y^2 + 50x = 75

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Question 439456: Find the vertices and foci of the conic. 25x^2 + 4y^2 + 50x = 75
Answer by Gogonati(809) About Me  (Show Source):
You can put this solution on YOUR website!
We rewrite the equation in the form:25x%5E2%2B50x%2B25%2B4y%5E2=75%2B25 simplify:
25%28x%2B1%29%5E2%2B4y%5E2=100, divide both sides by 100 and have:
%28x%2B1%29%5E2%2F4%2By%5E2%2F25=1, which is the equation of ellipse centered at (-1, 0).
the vertices are:(-1, 5) and (-1, -5).
The foci are: c%5E2=b%5E2-a%5E2 => c%5E2=25-4 => c=+/-sqrt(21) and the foci:
(-1, sqrt%2821%29) and (-1,-sqrt%2821%29).