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)?

1 Answer
Nov 17, 2015

Answer:

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

Explanation:

#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#