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    Topics || Problems

    Write the equation of the ellipse having an eccentricity equal to 1/3, a distance between foci equal to 2, center at origin and major axis parallel to the x-axis.

    \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), center at origin and major axis parallel to the x-axis.

    \(e = \frac{c}{a}\)

    Distance between foci is \(2c\) thus \(c = 1\).

    \(a = 3\)

    \(a^2 = b^2 +c^2\)

    \(3^2 = b^2 +1^2\)

    \(b = \sqrt{8}\)

    Thus the equation of the ellipse is, \(\frac{x^2}{9} + \frac{y^2}{8} = 1\)

    \(8x^2 + 9y^2 = 72\)