Question

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)?

Answer 1

`(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]}