How do you write an equation of an ellipse given the major axis is 16 units long and parallel to the x axis, minor axis 9 units long, center (5,4)?

1 Answer
Dec 13, 2017

Answer:

#(x-5)^2/64+(4(y-4)^2)/81=1#

Explanation:

The equation of an ellipse given its major axis as #2a# parallel to the #x#-axis, minor axis #2b# units long, obviusly parallels to #y#-axis and center #(h,k)# is

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

Here we have major axis #16# and hence #2a=16# or #a=8# and minor axis is #2b=9# or #b=9/2#. As center is #(5,4)#, the equation of ellipse is

#(x-5)^2/8^2+(y-4)^2/(9/2)^2=1#

or #(x-5)^2/64+(4(y-4)^2)/81=1#

graph{ (x-5)^2/8^2+(y-4)^2/(9/2)^2=1 [-5, 15, -1, 9]}