How do you find the coordinates of the center, foci, the length of the major and minor axis given #y^2/10+x^2/5=1#?

1 Answer
Oct 13, 2016

The center is #(0,0)#
The length of the major axis is #2sqrt(10)#
The length of the minor axis is #2sqrt(5)#
The foci are at #(0, sqrt(5))# and #(0, -sqrt(5))#

Explanation:

Please observe the denominator of the y term (10) is greater than the denominator of the x term (5). The standard form for an ellipse of this type is:

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

The center of the ellipse is the point #(h, k)#.
The value of #a# is the length of the semi-major axis and #2a# is the length of the major axis
The value of #b# is the length of the semi-minor axis and #2a# is the length of the minor axis.
The focal distance is, #c = sqrt(a^2 - b^2)#
The foci are located at #(h, k + c)# and #(h, k - c)#

Put the given equation in this form:

#(y - 0)^2/(sqrt(10))^2 + (x - 0)^2/(sqrt(5))^2 = 1#

The center is #(0,0)#
The length of the major axis is #2sqrt(10)#
The length of the minor axis is #2sqrt(5)#
The foci are at #(0, sqrt(5))# and #(0, -sqrt(5))#