What is 4x^2+3y^2+24x+36y+72=0 ?

The solution to 4x^2+3y^2+24x+36y+72=0 is Ellipse with (h,k)=(-3,-6),a=3sqrt(2),b=2sqrt(6)

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4x^2+3y^2+24x+36y+72=0

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0

(h, k) = (- 3, - 6), a = 32, b = 26

Solution steps

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0

Rewrite

4 x^{2} + 3 y^{2} + 24 x + 36 y + 72 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, - 6), a = 32, b = 26

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 3, - 6), b = 26, a = 32

a^{2} + 2 b^{2} = 10

\frac{x ^{2}}{12} + \frac{y ^{2}}{8} = 1

225 x^{2} + 576 y^{2} = 176400

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

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

What is 4x^2+3y^2+24x+36y+72=0 ?
The solution to 4x^2+3y^2+24x+36y+72=0 is Ellipse with (h,k)=(-3,-6),a=3sqrt(2),b=2sqrt(6)