What is 3x^2+12y^2+18x-24y-69=0 ?

The solution to 3x^2+12y^2+18x-24y-69=0 is Ellipse with (h,k)=(-3,1),a=6,b=3

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3x^2+12y^2+18x-24y-69=0

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

(h, k) = (- 3, 1), a = 6, b = 3

Solution steps

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

Rewrite

3 x^{2} + 12 y^{2} + 18 x - 24 y - 69 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{6 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), a = 6, b = 3

x^{2} + y^{2} = - 8 y

3 y^{2} + 5 x^{2} = 20

\frac{( x - 4 ) ^{2}}{36} + \frac{( y - 2 ) ^{2}}{20} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{8} = 1

4 x^{2} + 9 y^{2} + 24 x = 0

What is 3x^2+12y^2+18x-24y-69=0 ?
The solution to 3x^2+12y^2+18x-24y-69=0 is Ellipse with (h,k)=(-3,1),a=6,b=3