What is ((y+3)^2)/2-((x-1)^2)/(18)=1 ?

The solution to ((y+3)^2)/2-((x-1)^2)/(18)=1 is Hyperbola with (h,k)=(1,-3),a=sqrt(2),b=3sqrt(2)

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((y+3)^2)/2-((x-1)^2)/(18)=1

\frac{( y + 3 ) ^{2}}{2} - \frac{( x - 1 ) ^{2}}{18} = 1

(h, k) = (1, - 3), a = 2, b = 32

Solution steps

\frac{( y + 3 ) ^{2}}{2} - \frac{( x - 1 ) ^{2}}{18} = 1

Rewrite

\frac{( y + 3 ) ^{2}}{2} - \frac{( x - 1 ) ^{2}}{18} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 2, b = 32

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

x^{2} - 3 y^{2} + 11 x + y + 10 = 0

16 y^{2} - 4 x^{2} - 24 x - 12 y - 34 = 0

x^{2} + x - y^{2} = 5

(x - 8)^{2} - (y + 6)^{2} = 1

What is ((y+3)^2)/2-((x-1)^2)/(18)=1 ?
The solution to ((y+3)^2)/2-((x-1)^2)/(18)=1 is Hyperbola with (h,k)=(1,-3),a=sqrt(2),b=3sqrt(2)