Find the center, vertices, and foci of the ellipse 9x^2 + 4y^2 + 36x -8y + 4 =0  

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We start with writing the terms containing x and y together. We get 9x^2 + 36x + 4y^2 – 8y + 4 =0

=> 9(x^2 + 4x) + 4(y^2 – 2y) + 4 =0

Now complete the squares

=> 9(x^2 + 4x +4) +4(y^2 – 2y +1) = -4 + 36 + 4

(The entire section contains 108 words.)

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