What is 4y^2-2x^2+24y-8x-9=0 ?

The solution to 4y^2-2x^2+24y-8x-9=0 is Hyperbola with (h,k)=(-2,-3),a=(sqrt(37))/2 ,b=sqrt(37/2)

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4y^2-2x^2+24y-8x-9=0

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

(h, k) = (- 2, - 3), a = \frac{37}{2}, b = \frac{37}{2}

Solution steps

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

Rewrite

4 y^{2} - 2 x^{2} + 24 y - 8 x - 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( \frac{37}{2} ) ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{( \frac{37}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, - 3), a = \frac{37}{2}, b = \frac{37}{2}

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

7 p - p^{2} = 9 p + q^{2} - 16 - 5 q^{2} + 6

x^{2} - y^{2} < 8

9 y^{2} - 16 x^{2} = 1

4 x^{2} - 16 y^{2} - 10 x + 21 y - 27 = 0

What is 4y^2-2x^2+24y-8x-9=0 ?
The solution to 4y^2-2x^2+24y-8x-9=0 is Hyperbola with (h,k)=(-2,-3),a=(sqrt(37))/2 ,b=sqrt(37/2)