What is 3x^2+2y^2+12x-8y-16=0 ?

The solution to 3x^2+2y^2+12x-8y-16=0 is Ellipse with (h,k)=(-2,2),a=2sqrt(3),b=3sqrt(2)

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3x^2+2y^2+12x-8y-16=0

3 x^{2} + 2 y^{2} + 12 x - 8 y - 16 = 0

(h, k) = (- 2, 2), a = 23, b = 32

Solution steps

3 x^{2} + 2 y^{2} + 12 x - 8 y - 16 = 0

Rewrite

3 x^{2} + 2 y^{2} + 12 x - 8 y - 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 2), a = 23, b = 32

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 2), b = 32, a = 23

16 x^{2} + 25 y^{2} = 1.6

4 X^{2} + 9 Y^{2} - 32 X - 36 Y + 64 = 0

16 x^{2} + 9 y^{2} + 160 x + 18 y + 265 = 0

(\frac{x ^{2}}{16}) + (\frac{y ^{2}}{9}) = 1

x^{2} + \frac{y ^{2}}{25} = 1

What is 3x^2+2y^2+12x-8y-16=0 ?
The solution to 3x^2+2y^2+12x-8y-16=0 is Ellipse with (h,k)=(-2,2),a=2sqrt(3),b=3sqrt(2)