What is 10y^2-5x^2=50 ?

The solution to 10y^2-5x^2=50 is Hyperbola with (h,k)=(0,0),a=sqrt(5),b=sqrt(10)

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10y^2-5x^2=50

10 y^{2} - 5 x^{2} = 50

(h, k) = (0, 0), a = 5, b = 10

Solution steps

10 y^{2} - 5 x^{2} = 50

Rewrite

10 y^{2} - 5 x^{2} = 50

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 5 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 10 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 5, b = 10

y^{2} - 3 x^{2} - 4 x - 1 = 0

\frac{( x - 1 ) ^{2}}{4} - \frac{( y + 1 ) ^{2}}{9} = 1

\frac{x ^{2}}{8} - \frac{y ^{2}}{6} = 1

2 x^{2} - 4 y^{2} + 9 x - 15 y - 18 = 0

4 x^{2} - 32 x - y^{2} - 4 y + 24 = 0

What is 10y^2-5x^2=50 ?
The solution to 10y^2-5x^2=50 is Hyperbola with (h,k)=(0,0),a=sqrt(5),b=sqrt(10)