Question

How do you write `2(x+4)^2 + 3(y-1)^2 = 24` in standard form?

Answer 1

`(x-(-4))^2/(sqrt(12))^2 +(y-1)^2/(sqrt(8))^2=1`

Explanation:

The standard form for an ellipse is
`color(white)("XXX")(x-h)^2/a^2+(y-k)^2/b^2=1`

Given
`color(white)("XXX")2(x+4)^2+3(y-1)^2=24`

`rArr`
`color(white)("XXX")(x+4)^2/12+(y-1)^2/8=1`

`color(white)("XXX")(x-(-4))^2/(sqrt(12))^2+(y-1)^2/(sqrt(8))^2=1`

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If you like you could replace `(sqrt(12))^2` with `(2sqrt(3))^2`
and `(sqrt(8))^2` with `(2sqrt(2))^2`
...but this really doesn't make the form any simpler.