How do you write an equation of an ellipse in standard form given center (-1, 3) vertex (3,3) and minor axis of length 2?

1 Answer
Jan 26, 2016

Answer:

#(x+1)^2/16 + (y-3)^2/4 = 1#

Explanation:

The standard form for an ellipse is
#(x-h)^"/a^2 +(y-k)^2/b^2 = 1#
where #(h,k)# is the centre of the ellipse, #a# is the distance from the centre to the vertices and #c# is the distance from the centre to the foci. #b# is the minor axis.

# b^2+c^2 = a^2#

In this example #a = 3 - (-1) = 4# (The difference if the #x# coordinates of the centre and the vertex.)

The equations is #(x+1)^2/16 + (y-3)^2/4 = 1#