What is x^2-8y^2-6x-22y+4=0 ?

The solution to x^2-8y^2-6x-22y+4=0 is Hyperbola with (h,k)=(3,-11/8),a= 9/8 ,b= 9/(2sqrt(2))

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x^2-8y^2-6x-22y+4=0

x^{2} - 8 y^{2} - 6 x - 22 y + 4 = 0

(h, k) = (3, - \frac{11}{8}), a = \frac{9}{8}, b = \frac{9}{2 2}

Solution steps

x^{2} - 8 y^{2} - 6 x - 22 y + 4 = 0

Rewrite

x^{2} - 8 y^{2} - 6 x - 22 y + 4 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{11}{8} ) ) ^{2}}{( \frac{9}{8} ) ^{2}} - \frac{( x - 3 ) ^{2}}{( \frac{9}{2 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, - \frac{11}{8}), a = \frac{9}{8}, b = \frac{9}{2 2}

\frac{( y - 11 ) ^{2}}{16} - \frac{( x + 5 ) ^{2}}{36} = 1

- 25 x^{2} + y^{2} = 25

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

a = \frac{2020 - c}{\frac{2021 - a}{c}}

5 y^{2} - 9 x^{2} = 45

What is x^2-8y^2-6x-22y+4=0 ?
The solution to x^2-8y^2-6x-22y+4=0 is Hyperbola with (h,k)=(3,-11/8),a= 9/8 ,b= 9/(2sqrt(2))