What is 36x^2-y^2-216x+10y+263=0 ?

The solution to 36x^2-y^2-216x+10y+263=0 is Hyperbola with (h,k)=(3,5),a=1,b=6

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36x^2-y^2-216x+10y+263=0

36 x^{2} - y^{2} - 216 x + 10 y + 263 = 0

(h, k) = (3, 5), a = 1, b = 6

Solution steps

36 x^{2} - y^{2} - 216 x + 10 y + 263 = 0

Rewrite

36 x^{2} - y^{2} - 216 x + 10 y + 263 = 0

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{1 ^{2}} - \frac{( y - 5 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, 5), a = 1, b = 6

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

\frac{x ^{2}}{16} - \frac{( y + 4 ) ^{2}}{81} = 1

9 x^{2} - 4 y^{2} - 36 x + 8 y - 4 = 0

y^{2} = x^{2} - 2

16 x^{2} - 20 y^{2} - 320 = 0

What is 36x^2-y^2-216x+10y+263=0 ?
The solution to 36x^2-y^2-216x+10y+263=0 is Hyperbola with (h,k)=(3,5),a=1,b=6