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

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

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

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

(h, k) = (0, 0), a = 2, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} - \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2, b = 5

y^{2} = x^{2} + 529

x^{2} + 79 = y^{2} + 18 x - 2 y

4 x^{2} - 4 y^{2} + 20 x - 16 y + 25 = 0

\frac{( x ^{(2)} )}{( 25 )} - \frac{( y ^{(2)} )}{( 11 )} = 1

a^{2} - b^{2} - 4 a + 2 b = 19

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