How do you write an equation of an ellipse in standard form given vertices are (plus or minus 15,0) and the foci are (plus or minus 9,0)?

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Answer 1 · 2015-11-17T16:43:32

$x^2/225 + y^2/144 = 1$

$V: (+-15, 0)$

$V: (h +- a, k)$

$=> V: ( 0 +- 15, 0)$

$=> C: (h, k) => (0, 0)$

$a = 15$

$f: (h +- c, k)$

$f: (+-9, 0)$

$=> c = 9$

$c^2 = a^2 - b^2$

$=> b^2 = a^2 - c^2$

$=> b^2 = 15^2 - 9^2$

$=> b^2 = 225 - 81 = 144$

$=> b = 12$

Standard equation of a horizontal ellipse is

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

$=> (x - 0)^2/15^2 + (y - 0)^2/9^2 = 1$

$=> x^2/225 + y^2/144 = 1$