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

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Answer 1 · 2018-03-30T13:55:29

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

$2(x+4)^2+3(y-1)^2=24$ - 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]}

How do you write the Ellipse equation in standard form 2(x+4)^2 + 3(y-1)^2 = 242(x+4)^2 + 3(y-1)^2 = 24?