What is 9x^2+36y^2+54x-288y+333=0 ?

The solution to 9x^2+36y^2+54x-288y+333=0 is Ellipse with (h,k)=(-3,4),a=6,b=3

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9x^2+36y^2+54x-288y+333=0

9 x^{2} + 36 y^{2} + 54 x - 288 y + 333 = 0

(h, k) = (- 3, 4), a = 6, b = 3

Solution steps

9 x^{2} + 36 y^{2} + 54 x - 288 y + 333 = 0

Rewrite

9 x^{2} + 36 y^{2} + 54 x - 288 y + 333 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 3 ) ) ^{2}}{6 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 3, 4), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 3, 4), a = 6, b = 3

25 x^{2} + 9 y^{2} - 10 y - 216 = 0

(36 - 4 x^{2} - 9 y^{2}) = 0

\frac{( x - 5 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 900 = 0

\frac{x ^{2}}{36} + \frac{( y + 1 ) ^{2}}{25} = 1

What is 9x^2+36y^2+54x-288y+333=0 ?
The solution to 9x^2+36y^2+54x-288y+333=0 is Ellipse with (h,k)=(-3,4),a=6,b=3