What is x^2=(13y^2+1) ?

The solution to x^2=(13y^2+1) is Hyperbola with (h,k)=(0,0),a=1,b=sqrt(1/13)

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x^2=(13y^2+1)

x^{2} = (13 y^{2} + 1)

(h, k) = (0, 0), a = 1, b = \frac{1}{13}

Solution steps

x^{2} = (13 y^{2} + 1)

Rewrite

x^{2} = (13 y^{2} + 1)

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{13} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 1, b = \frac{1}{13}

a^{2} - b^{2} = 424

a^{2} - b^{2} = 415

4 y^{2} - 24 y - 2 x^{2} + 20 = 2

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

\frac{( y - 9 ) ^{2}}{45} - \frac{( x + 3 ) ^{2}}{\frac{45}{2}} = 1

What is x^2=(13y^2+1) ?
The solution to x^2=(13y^2+1) is Hyperbola with (h,k)=(0,0),a=1,b=sqrt(1/13)