What is 2x^2+3y^2+12x-24y+60=0 ?

The solution to 2x^2+3y^2+12x-24y+60=0 is Ellipse with (h,k)=(-3,4),a=sqrt(3),b=sqrt(2)

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2x^2+3y^2+12x-24y+60=0

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

(h, k) = (- 3, 4), a = 3, b = 2

Solution steps

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

Rewrite

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{( 3 ) ^{2}} + \frac{( y - 4 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 3, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), a = 3, b = 2

\frac{x ^{2}}{4} + \frac{( y - 1 ) ^{2}}{9} < 1

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

4 x^{2} + 25 y^{2} - 24 x + 250 y + 561 = 0

x^{2} + 9 y^{2} - 18 y = 0

100 x^{2} + 64 y^{2} = 1600

What is 2x^2+3y^2+12x-24y+60=0 ?
The solution to 2x^2+3y^2+12x-24y+60=0 is Ellipse with (h,k)=(-3,4),a=sqrt(3),b=sqrt(2)