What is y^2+1=4x^2+(-1) ?

The solution to y^2+1=4x^2+(-1) is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(2)

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

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

(h, k) = (0, 0), a = \frac{1}{2}, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = 2

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

36 x^{2} - 4 y^{2} - 36 x - 8 y = 31

\frac{( x - 3 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{9} = 1

9 x^{2} - 4 y^{2} + 54 x + 16 y + 29 = 0

y^{2} - 9 x^{2} = 9

What is y^2+1=4x^2+(-1) ?
The solution to y^2+1=4x^2+(-1) is Hyperbola with (h,k)=(0,0),a=sqrt(1/2),b=sqrt(2)