What is 3x^2+4y^2+18x+8y+19=0 ?

The solution to 3x^2+4y^2+18x+8y+19=0 is Ellipse with (h,k)=(-3,-1),a=2,b=sqrt(3)

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3x^2+4y^2+18x+8y+19=0

3 x^{2} + 4 y^{2} + 18 x + 8 y + 19 = 0

(h, k) = (- 3, - 1), a = 2, b = 3

Solution steps

3 x^{2} + 4 y^{2} + 18 x + 8 y + 19 = 0

Rewrite

3 x^{2} + 4 y^{2} + 18 x + 8 y + 19 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 1), a = 2, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 1), a = 2, b = 3

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{16} = 1

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

\frac{- x ^{2}}{2 ^{2}} - \frac{y ^{2}}{4 ^{2}} = 1

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 8 ) ^{2}}{16} = 1

36 (x + 2)^{2} + (y - 4)^{2} = 72

What is 3x^2+4y^2+18x+8y+19=0 ?
The solution to 3x^2+4y^2+18x+8y+19=0 is Ellipse with (h,k)=(-3,-1),a=2,b=sqrt(3)