What is 25y^{(2)}-16x^{(2)}-400=0 ?

The solution to 25y^{(2)}-16x^{(2)}-400=0 is Hyperbola with (h,k)=(0,0),a=4,b=5

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25y^{(2)}-16x^{(2)}-400=0

25 y^{(2)} - 16 x^{(2)} - 400 = 0

(h, k) = (0, 0), a = 4, b = 5

Solution steps

25 y^{2} - 16 x^{2} - 400 = 0

Rewrite

25 y^{2} - 16 x^{2} - 400 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{4 ^{2}} - \frac{( x - 0 ) ^{2}}{5 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 4, b = 5

- x^{2} + 4 y^{2} = 4

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

x^{2} + 24 = y^{2} + 6 x - 2 y

x^{2} - y^{2} + 10 x - 6 y = 2

x^{2} - y^{2} = 200 0^{2}

What is 25y^{(2)}-16x^{(2)}-400=0 ?
The solution to 25y^{(2)}-16x^{(2)}-400=0 is Hyperbola with (h,k)=(0,0),a=4,b=5