Question

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

Answer 1

`(x+4)^2/(sqrt12)^2+(y-1)^2/(sqrt8)^2=1`

Explanation:

`2(x+4)^2+3(y-1)^2=24` - dividing by `24`, it can be written as

`(2(x+4)^2)/24+(3(y-1)^2)/24=1`

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

or `(x+4)^2/(sqrt12)^2+(y-1)^2/(sqrt8)^2=1`

which is the equation of an ellipse with center at `(-4,1)`,

major axis parallel to `x`-axis is `2sqrt12=4sqrt3`

and minor axis parallel to `y`-axis is `2sqrt8=4sqrt2`

graph{((x+4)^2/12+(y-1)^2/8-1)((x+4)^2+(y-1)^2-0.01)=0 [-11, 3, -2.5, 4.5]}