What is 25x^2-4y^2-100x-16y-16=0 ?

The solution to 25x^2-4y^2-100x-16y-16=0 is Hyperbola with (h,k)=(2,-2),a=2,b=5

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25x^2-4y^2-100x-16y-16=0

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

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

Solution steps

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

Rewrite

25 x^{2} - 4 y^{2} - 100 x - 16 y - 16 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - 5 y^{2} = 25

\frac{y ^{2}}{100} - \frac{x ^{2}}{36} = 1

\frac{y ^{2}}{36} - \frac{x ^{2}}{9} = 1

12 x^{2} - 4 y^{2} - 72 x - 16 y + 44 = 0

- x^{2} + 36 z^{2} = 9

What is 25x^2-4y^2-100x-16y-16=0 ?
The solution to 25x^2-4y^2-100x-16y-16=0 is Hyperbola with (h,k)=(2,-2),a=2,b=5