What is 27x^2+36y^2+108x-144y-720=0 ?

The solution to 27x^2+36y^2+108x-144y-720=0 is Ellipse with (h,k)=(-2,2),a=6,b=3sqrt(3)

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27x^2+36y^2+108x-144y-720=0

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

(h, k) = (- 2, 2), a = 6, b = 33

Solution steps

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

Rewrite

27 x^{2} + 36 y^{2} + 108 x - 144 y - 720 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 2), a = 6, b = 33

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 2), a = 6, b = 33

\frac{x ^{2}}{2 ^{2}} + \frac{y ^{2}}{2 - 16} = 1

6 = 8 x^{2} + y^{2}

4 x^{2} + 7 y^{2} < 28

x^{2} + 9 y^{2} - 8 x + 36 y - 2 = 0

3 x^{2} + 9 x + y^{2} = 36 - (2 x^{2} + y^{2} - 3 x)

What is 27x^2+36y^2+108x-144y-720=0 ?
The solution to 27x^2+36y^2+108x-144y-720=0 is Ellipse with (h,k)=(-2,2),a=6,b=3sqrt(3)