What is (x-3)^2=8+(y+5)^2 ?

The solution to (x-3)^2=8+(y+5)^2 is Hyperbola with (h,k)=(3,-5),a=2sqrt(2),b=2sqrt(2)

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(x-3)^2=8+(y+5)^2

(x - 3)^{2} = 8 + (y + 5)^{2}

(h, k) = (3, - 5), a = 22, b = 22

Solution steps

(x - 3)^{2} = 8 + (y + 5)^{2}

Rewrite

(x - 3)^{2} - 8 - (y + 5)^{2} = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (3, - 5), a = 22, b = 22

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

4 x^{2} + 8 x - 4 y^{2} + 12 y - 3 = 0

\frac{( x + 4 ) ^{2}}{16} - \frac{( y - 2 ) ^{2}}{36} = 1

12 y^{2} + 72 y - 4 x^{2} + 16 x + 44 = 0

(x - 1)^{2} - (y - 4)^{2} = 16

What is (x-3)^2=8+(y+5)^2 ?
The solution to (x-3)^2=8+(y+5)^2 is Hyperbola with (h,k)=(3,-5),a=2sqrt(2),b=2sqrt(2)