What is y^2-9x^2-4y+18x=86 ?

The solution to y^2-9x^2-4y+18x=86 is Hyperbola with (h,k)=(1,2),a=9,b=3

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y^2-9x^2-4y+18x=86

y^{2} - 9 x^{2} - 4 y + 18 x = 86

(h, k) = (1, 2), a = 9, b = 3

Solution steps

y^{2} - 9 x^{2} - 4 y + 18 x = 86

Rewrite

y^{2} - 9 x^{2} - 4 y + 18 x = 86

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 2), a = 9, b = 3

y^{2} - 4 x^{2} + 8 x = 20 y + 4

\frac{x ^{2}}{4} - \frac{y ^{2}}{32} = 1

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

4 y^{2} - 3 x^{2} - 8 y + 6 x - 3 = 0

- x^{2} + 9 y^{2} + 90 y + 189 = 0

What is y^2-9x^2-4y+18x=86 ?
The solution to y^2-9x^2-4y+18x=86 is Hyperbola with (h,k)=(1,2),a=9,b=3