What is x^2=y^2-13+14x ?

The solution to x^2=y^2-13+14x is Hyperbola with (h,k)=(7,0),a=6,b=6

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x^2=y^2-13+14x

x^{2} = y^{2} - 13 + 14 x

(h, k) = (7, 0), a = 6, b = 6

Solution steps

x^{2} = y^{2} - 13 + 14 x

Rewrite

x^{2} = y^{2} - 13 + 14 x

in the form of a standard hyperbola equation

\frac{( x - 7 ) ^{2}}{6 ^{2}} - \frac{( y - 0 ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (7, 0), a = 6, b = 6

x^{2} - y^{2} \leq 1

64 x^{2} + 128 x - 9 y^{2} - 72 y - 656 = 0

x^{2} - 3 y^{2} - 2 x = 0

\frac{( x + 5 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{16} = 1

6 x^{2} - 9 y^{2} + 96 x + 36 y + 252 = 0

What is x^2=y^2-13+14x ?
The solution to x^2=y^2-13+14x is Hyperbola with (h,k)=(7,0),a=6,b=6