What is 4x^2-25y^2-40x-150y-225=0 ?

The solution to 4x^2-25y^2-40x-150y-225=0 is Hyperbola with (h,k)=(5,-3),a=5,b=2

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4x^2-25y^2-40x-150y-225=0

4 x^{2} - 25 y^{2} - 40 x - 150 y - 225 = 0

(h, k) = (5, - 3), a = 5, b = 2

Solution steps

4 x^{2} - 25 y^{2} - 40 x - 150 y - 225 = 0

Rewrite

4 x^{2} - 25 y^{2} - 40 x - 150 y - 225 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (5, - 3), a = 5, b = 2

4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

(x + k (x)) (x - k (x)) = k (x)

\frac{x ^{2}}{16} - \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{64} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

What is 4x^2-25y^2-40x-150y-225=0 ?
The solution to 4x^2-25y^2-40x-150y-225=0 is Hyperbola with (h,k)=(5,-3),a=5,b=2