What is -8x^2+y^2-36x+6y-27=0 ?

The solution to -8x^2+y^2-36x+6y-27=0 is Hyperbola with (h,k)=(-9/4 ,-3),a= 3/4 ,b= 3/(sqrt(2))

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-8x^2+y^2-36x+6y-27=0

- 8 x^{2} + y^{2} - 36 x + 6 y - 27 = 0

(h, k) = (- \frac{9}{4}, - 3), a = \frac{3}{4}, b = \frac{3}{2}

Solution steps

- 8 x^{2} + y^{2} - 36 x + 6 y - 27 = 0

Rewrite

- 8 x^{2} + y^{2} - 36 x + 6 y - 27 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- \frac{9}{4}, - 3), a = \frac{3}{4}, b = \frac{3}{2}

x^{2} + 1 - 2 y^{2} = 0

9 y^{2} - 16 x^{2} - 18 y - 64 x - 199 = 0

6 y^{2} - 3 x^{2} = 6

9 y^{2} - 16 x^{2} - 64 x - 54 y - 127 = 0

y^{2} = x^{2} + 2 x - 15

What is -8x^2+y^2-36x+6y-27=0 ?
The solution to -8x^2+y^2-36x+6y-27=0 is Hyperbola with (h,k)=(-9/4 ,-3),a= 3/4 ,b= 3/(sqrt(2))