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Ellipse and Hyperbola

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Find the equation of the Ellipse whose foci coincide with the foci of the hyperbola x^2 - 3y^2 - 2x - 12y + 1 = 0 and whose eccentricity is the reciprocal of that of the hyperbola and sketch both curves.

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The expert examines ellipse and hyperbola. Neat and Detailed solution. Graph included.

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x^2 - 2x + 1 - 3y^2 - 12y = 0
(x^2 - 2x + 1) - 3(y^2 + 4y + 4) = -12
(x - 1)^2 - 3(y + 2)^2 = -12
(x - 1)^2 /12 - (y + 2)^2 /4 = -1
This is a conjugate hyperbola with its:
Semi transverse axis = b = 2 and semi ...

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