What is x^2-y^2-8x-14y-49=0 ?

The solution to x^2-y^2-8x-14y-49=0 is Hyperbola with (h,k)=(4,-7),a=4,b=4

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x^2-y^2-8x-14y-49=0

x^{2} - y^{2} - 8 x - 14 y - 49 = 0

(h, k) = (4, - 7), a = 4, b = 4

Solution steps

x^{2} - y^{2} - 8 x - 14 y - 49 = 0

Rewrite

x^{2} - y^{2} - 8 x - 14 y - 49 = 0

in the form of a standard hyperbola equation

\frac{( x - 4 ) ^{2}}{4 ^{2}} - \frac{( y - ( - 7 ) ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (4, - 7), a = 4, b = 4

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

[f (x)]^{2} = 2 x^{2} - x + 5

\frac{( x + 4 ) ^{2}}{64} - \frac{( y + 5 ) ^{2}}{81} = 1

3 x^{(2)} - 12 y^{(2)} + 48 = 0

- 9 y^{2} + z^{2} = 36

What is x^2-y^2-8x-14y-49=0 ?
The solution to x^2-y^2-8x-14y-49=0 is Hyperbola with (h,k)=(4,-7),a=4,b=4