What is 3x^2+y^2+18x-2y-8=0 ?

The solution to 3x^2+y^2+18x-2y-8=0 is Ellipse with (h,k)=(-3,1),a=2sqrt(3),b=6

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3x^2+y^2+18x-2y-8=0

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

(h, k) = (- 3, 1), a = 23, b = 6

Solution steps

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

Rewrite

3 x^{2} + y^{2} + 18 x - 2 y - 8 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 1), a = 23, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, 1), b = 6, a = 23

\frac{x ^{2}}{5} + \frac{y ^{2}}{9} = 1

3 x^{2} + 2 y^{2} = 6

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

y^{2} + 20 x + 8 y + 56 = 0

x^{2} + y^{2} \leq 16

What is 3x^2+y^2+18x-2y-8=0 ?
The solution to 3x^2+y^2+18x-2y-8=0 is Ellipse with (h,k)=(-3,1),a=2sqrt(3),b=6