What is 5y^{(2)}-16x^{(2)}-400=0 ?

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

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5y^{(2)}-16x^{(2)}-400=0

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

(h, k) = (0, 0), a = 45, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 45, b = 5

x^{2} - y^{2} + 7 x + 8 y - 5 = 0

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

2 x^{2} - 4 y^{2} + 12 x + 8 y + 10 = 0

\frac{x ^{2}}{11} - \frac{y ^{2}}{16} = 1

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

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