What is 3x^2+4y^2+6x-24y+27=0 ?

The solution to 3x^2+4y^2+6x-24y+27=0 is Ellipse with (h,k)=(-1,3),a=2,b=sqrt(3)

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3x^2+4y^2+6x-24y+27=0

3 x^{2} + 4 y^{2} + 6 x - 24 y + 27 = 0

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

Solution steps

3 x^{2} + 4 y^{2} + 6 x - 24 y + 27 = 0

Rewrite

3 x^{2} + 4 y^{2} + 6 x - 24 y + 27 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} + 9 y^{2} - 100 x + 18 x - 10 y - 31 = 0

- X^{2} - 4 = Y^{2}

8 y^{2} = - \frac{9}{2} x^{2} + \frac{25}{2}

x^{2} + 3 y^{2} = 28

12 x^{2} + 3 y^{2} + 12 y - 96 = 0

What is 3x^2+4y^2+6x-24y+27=0 ?
The solution to 3x^2+4y^2+6x-24y+27=0 is Ellipse with (h,k)=(-1,3),a=2,b=sqrt(3)