Question

How do you find the coordinates of the center, foci, the length of the major and minor axis given `16x^2+9y^2=144`?

Answer 1

Center is `(0,0)`, focii are `(0,sqrt7)` and `(0,-sqrt7)`, major axis is along `y`-axis and is `8`, and minor axis is along `x`-axis and is `6`.

Explanation:

Note that equation `16x^2+9y^2=144` by dividing each term by `144` can be written as `x^2/9+y^2/16=1`

As the standard equation is of the form `x^2/a^2+y^2/b^2=1`, center is `(0,0)`.

In this equation major axis is along `y`-axis and is `2b=8`, and minor axis is along `x`-axis and is `2a=6`.

As `a=3` and `b=4`, focii are given by `+-sqrt(4^2-3^2)=+-sqrt7` i.e. `(0,sqrt7)` and `(0,-sqrt7)`
graph{16x^2+9y^2=144 [-10, 10, -5, 5]}