How do you find the center, vertices, and foci of an ellipse #(1/16)(x + 2)^2 + (1/9)(y - 5)^2 = 1#?

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Answer 1 · 2015-11-17T21:33:33

See explanation

Standard equation of an ellipse

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

or

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

where #a > b#

Since the denominator of the #x# is larger, we use the first equation

#C: (h, k) => (-2, 5)#

#V: (h +- a, k) => (-2 +- 4, 5)#

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

where # c^2 = a^2 - b^2#

#=> c^2 = 16 - 9 => 7#
#=> c = sqrt7#

#=> f: (-2 +- sqrt7, 5)#