How do you find the coordinates of the center, foci, the length of the major and minor axis given #x^2/25+y^2/9=1#?

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Answer 1 · 2016-11-14T03:01:48

Please see the explanation

The standard form for an ellipse is:

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

The centerpoint is:

#(h, k)#

The vertices are at:

#(h - a, k), (h + a, k), (h, k - b), and (h, k + b)#

If #a > b# then the foci are at:

#(h - sqrt(a^2-b^2), k) and (h + sqrt(a^2 - b^2), k)#

The length of the major axis is #2a#

The length of the minor axis is #2b#

If #b > a# then the foci are at:

#(h, k - sqrt(b^2-a^2)) and (h, k + sqrt(b^2 - a^2))#

The length of the major axis is #2b#

The length of the minor axis is #2a#

Convert the given equation to standard form:

#(x - 0)^2/5^2 + (y - 0)^2/3^2 = 1#

The centerpoint is:

#(0, 0)#

The vertices are at:

#(-5, 0), (5, 0), (0, -3), and (0, 3)#

#a > b# then the foci are at:

#(-4, 0) and (4, 0)#

The length of the major axis is #10#

The length of the minor axis is #6#