What is -81x^2+486x+64y^2+128y+4519=0 ?

The solution to -81x^2+486x+64y^2+128y+4519=0 is Hyperbola with (h,k)=(3,-1),a=8,b=9

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-81x^2+486x+64y^2+128y+4519=0

- 81 x^{2} + 486 x + 64 y^{2} + 128 y + 4519 = 0

(h, k) = (3, - 1), a = 8, b = 9

Solution steps

- 81 x^{2} + 486 x + 64 y^{2} + 128 y + 4519 = 0

Rewrite

- 81 x^{2} + 486 x + 64 y^{2} + 128 y + 4519 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{8 ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{9 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, - 1), a = 8, b = 9

- 2 x^{2} + y^{2} + 20 x + 6 y - 45 = 0

\frac{y ^{2}}{80} - \frac{x ^{2}}{4} = 1

\frac{( y + 6 ) ^{2}}{25} - (x - 2)^{2} = 1

y^{2} \leq x^{2} - 1

7 x^{2} - 7 y^{2} + 5 x - 10 y + 22 = 0

What is -81x^2+486x+64y^2+128y+4519=0 ?
The solution to -81x^2+486x+64y^2+128y+4519=0 is Hyperbola with (h,k)=(3,-1),a=8,b=9