What is x^2-y^2+6x+8y-75=0 ?

The solution to x^2-y^2+6x+8y-75=0 is Hyperbola with (h,k)=(-3,4),a=2sqrt(17),b=2sqrt(17)

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x^2-y^2+6x+8y-75=0

x^{2} - y^{2} + 6 x + 8 y - 75 = 0

(h, k) = (- 3, 4), a = 217, b = 217

Solution steps

x^{2} - y^{2} + 6 x + 8 y - 75 = 0

Rewrite

x^{2} - y^{2} + 6 x + 8 y - 75 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( 2 17 ) ^{2}} - \frac{( y - 4 ) ^{2}}{( 2 17 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 4), a = 217, b = 217

\frac{x ^{2}}{25} - \frac{y ^{2}}{1} = 1

z^{2} = \frac{y + 5}{9} + 5 + y \cdot \frac{y + 5}{9}

x^{2} - 4 y^{2} - 4 x = 0

y^{2} - 5 x^{2} = 90

X^{2} - 4 = Y^{2}

What is x^2-y^2+6x+8y-75=0 ?
The solution to x^2-y^2+6x+8y-75=0 is Hyperbola with (h,k)=(-3,4),a=2sqrt(17),b=2sqrt(17)