What is x^2+42x+441=72y+y^2 ?

The solution to x^2+42x+441=72y+y^2 is Hyperbola with (h,k)=(-21,-36),a=36,b=36

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x^2+42x+441=72y+y^2

x^{2} + 42 x + 441 = 72 y + y^{2}

(h, k) = (- 21, - 36), a = 36, b = 36

Solution steps

x^{2} + 42 x + 441 = 72 y + y^{2}

Rewrite

x^{2} + 42 x + 441 = 72 y + y^{2}

in the form of a standard hyperbola equation

\frac{( y - ( - 36 ) ) ^{2}}{3 6 ^{2}} - \frac{( x - ( - 21 ) ) ^{2}}{3 6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 21, - 36), a = 36, b = 36

\frac{( x - 5 ) ^{2}}{9} - \frac{( y - 4 ) ^{2}}{25} = 1

x, h (x)^{2} = (5)^{2} + (12)^{2} + (x)^{2}

4 x^{2} - y^{2} - 20 x - 10 y - 25 = 0

18 x^{2} - 32 y^{2} - 108 y - 128 x - 254 = 0^{2}

\frac{x ^{2}}{5} - \frac{y ^{2}}{1} = 1

What is x^2+42x+441=72y+y^2 ?
The solution to x^2+42x+441=72y+y^2 is Hyperbola with (h,k)=(-21,-36),a=36,b=36