What is x^2-y^2+7x+8y=5 ?

The solution to x^2-y^2+7x+8y=5 is Hyperbola with (h,k)=(-7/2 ,4),a=(sqrt(5))/2 ,b=(sqrt(5))/2

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x^2-y^2+7x+8y=5

x^{2} - y^{2} + 7 x + 8 y = 5

(h, k) = (- \frac{7}{2}, 4), a = \frac{5}{2}, b = \frac{5}{2}

Solution steps

x^{2} - y^{2} + 7 x + 8 y = 5

Rewrite

x^{2} - y^{2} + 7 x + 8 y = 5

in the form of a standard hyperbola equation

\frac{( x - ( - \frac{7}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} - \frac{( y - 4 ) ^{2}}{( \frac{5}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{7}{2}, 4), a = \frac{5}{2}, b = \frac{5}{2}

x^{2} - (y - 3)^{2} = 16

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

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

x^{2} - 9 y^{2} + 4 x + 18 y - 149 = 0

4 y^{2} - 24 y - 2 x^{2} + 20 x = 22

What is x^2-y^2+7x+8y=5 ?
The solution to x^2-y^2+7x+8y=5 is Hyperbola with (h,k)=(-7/2 ,4),a=(sqrt(5))/2 ,b=(sqrt(5))/2