How do you write an equation of an ellipse in standard form given center is at origin, major axis is 18 minor axis is 6?

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Answer 1 · 2015-11-15T14:31:24

$x^2/81 + y^2/9 = 1$ if the major axis is horizontal
$x^2/9 + y^2/81 = 1$ if the major axis is vertical

$C: (0, 0)$

$M = 18 = 2a => a = 9$

$m = 6 = 2b => b = 3$

If the major axis is horizontal, the standard equation of the ellipse is

$(x - h)^2/a^2 + (y - k)^2/b^2 = 1$

$=> (x - 0)^2/9^2 + (y - 0)^2/3^2 = 1$

$=> x^2/81 + y^2/9 = 1$

If the major axis is vertical, the standard equation of the ellipse is

$(x - h)^2/b^2 + (y - k)^2/a^2 = 1$

$=> (x - 0)^2/3^2 + (y - 0)^2/9^2 = 1$

$=> x^2/9 + y^2/81 = 1$