Question

How do you write the equation of each conic section ellipse with x-intercepts at (4, 0) and (-4, 0) and y-intercepts at (0, 1) and (0, -1)?

Answer 1

`(x/4)^{2}+(y/1)^{2}=1`, which can also be written as `x^{2}/16+y^{2}=1` or as `x^{2}+16y^{2}=16`.

Explanation:

An equation of an ellipse with `x`-intercepts at `(\pm a,0)` and `y`-intercepts at `(0,pm b)` can be written as `(x/a)^{2}+(y/b)^{2}=1`, or `x^{2}/a^{2}+y^{2}/b^{2}=1`.

You can see that this works by plugging in `y=0` and solving for `x` and plugging in `x=0` and solving for `y`.