What is 4x^2+12y^2+24x+48y+36=0 ?

The solution to 4x^2+12y^2+24x+48y+36=0 is Ellipse with (h,k)=(-3,-2),a=2sqrt(3),b=2

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4x^2+12y^2+24x+48y+36=0

4 x^{2} + 12 y^{2} + 24 x + 48 y + 36 = 0

(h, k) = (- 3, - 2), a = 23, b = 2

Solution steps

4 x^{2} + 12 y^{2} + 24 x + 48 y + 36 = 0

Rewrite

4 x^{2} + 12 y^{2} + 24 x + 48 y + 36 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 2), a = 23, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 2), a = 23, b = 2

4 x^{2} + 36 y^{2} + 40 x - 72 y - 8 = 0

\frac{x ^{2}}{9} + \frac{( y - 3 ) ^{2}}{25} = 1

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

9 x^{2} + 16 y^{2} - 90 x + 256 y + 1105 = 0

9 x^{2} + 25 y^{2} - 18 x - 110 y - 116 = 0

What is 4x^2+12y^2+24x+48y+36=0 ?
The solution to 4x^2+12y^2+24x+48y+36=0 is Ellipse with (h,k)=(-3,-2),a=2sqrt(3),b=2