What is y^2=(-x)^2+6 ?

The solution to y^2=(-x)^2+6 is Hyperbola with (h,k)=(0,0),a=sqrt(6),b=sqrt(6)

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y^2=(-x)^2+6

y^{2} = (- x)^{2} + 6

(h, k) = (0, 0), a = 6, b = 6

Solution steps

y^{2} = (- x)^{2} + 6

Rewrite

y^{2} - (- x)^{2} - 6 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 6, b = 6

\frac{4 b - 4 a}{b - a} = (a^{2} - b^{2})

\frac{x ^{2}}{25} - y^{2} = 1

\frac{( x - 3 ) ^{2}}{49} - \frac{( y + 5 ) ^{2}}{25} = 1

9 x^{2} - y^{2} - 36 x - 6 y + 18 = 0

\frac{( x + 4 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{25} = 1

What is y^2=(-x)^2+6 ?
The solution to y^2=(-x)^2+6 is Hyperbola with (h,k)=(0,0),a=sqrt(6),b=sqrt(6)