Question

How do you find the standard form of `x^2/81 + 4y/9 = 1` and what kind of a conic is it?

Answer 1

`y=-1/36x^2+9/4` which is a parabola with a vertical axis of symmetry and a vertex at `(0,9/4)`

Explanation:

`(x^2)/81+4y/9=1`

`rArrcolor(white)("XX")4y/9=1-x^2/81`

`rArrcolor(white)("XX")y=9/4(1-x^2/81)`

`rArrcolor(white)("XX")y=-1/36x^2+9/4`

graph{x^2/81+4y/9=1 [-16.03, 16.01, -8, 8.03]}