What is ((y-4)^2}{48}-\frac{(x+1)^2)/9 =1 ?

The solution to ((y-4)^2}{48}-\frac{(x+1)^2)/9 =1 is Hyperbola with (h,k)=(-1,4),a=4sqrt(3),b=3

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((y-4)^2}{48}-\frac{(x+1)^2)/9 =1

\frac{( y - 4 ) ^{2}}{48} - \frac{( x + 1 ) ^{2}}{9} = 1

(h, k) = (- 1, 4), a = 43, b = 3

Solution steps

\frac{( y - 4 ) ^{2}}{48} - \frac{( x + 1 ) ^{2}}{9} = 1

Rewrite

\frac{( y - 4 ) ^{2}}{48} - \frac{( x + 1 ) ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 4), a = 43, b = 3

25 y^{(2)} - 16 x^{(2)} - 400 = 0

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

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

x^{2} + 24 = y^{2} + 6 x - 2 y

x^{2} - y^{2} + 10 x - 6 y = 2

What is ((y-4)^2}{48}-\frac{(x+1)^2)/9 =1 ?
The solution to ((y-4)^2}{48}-\frac{(x+1)^2)/9 =1 is Hyperbola with (h,k)=(-1,4),a=4sqrt(3),b=3