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#