What is -9x^2+25y^2-72x-144-100y=0 ?

The solution to -9x^2+25y^2-72x-144-100y=0 is Hyperbola with (h,k)=(-4,2),a=2,b= 10/3

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-9x^2+25y^2-72x-144-100y=0

- 9 x^{2} + 25 y^{2} - 72 x - 144 - 100 y = 0

(h, k) = (- 4, 2), a = 2, b = \frac{10}{3}

Solution steps

- 9 x^{2} + 25 y^{2} - 72 x - 144 - 100 y = 0

Rewrite

- 9 x^{2} + 25 y^{2} - 72 x - 144 - 100 y = 0

in the form of a standard hyperbola equation

\frac{( y - 2 ) ^{2}}{2 ^{2}} - \frac{( x - ( - 4 ) ) ^{2}}{( \frac{10}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, 2), a = 2, b = \frac{10}{3}

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

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

x^{2} - \frac{1}{3} y^{2} = x + y

x^{2} - y^{2} + 1 = 0

x, x^{2} - 48 x + 640 = m (x)^{2}

What is -9x^2+25y^2-72x-144-100y=0 ?
The solution to -9x^2+25y^2-72x-144-100y=0 is Hyperbola with (h,k)=(-4,2),a=2,b= 10/3