What is 4y^2-24y-2x^2+20=2 ?

The solution to 4y^2-24y-2x^2+20=2 is Hyperbola with (h,k)=(0,3),a= 3/(sqrt(2)),b=3

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4y^2-24y-2x^2+20=2

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

(h, k) = (0, 3), a = \frac{3}{2}, b = 3

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{3 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 3), a = \frac{3}{2}, b = 3

9 (x^{2} - 2 x) - 4 (y^{2} + 4 y) = - 29

\frac{( y - 9 ) ^{2}}{45} - \frac{( x + 3 ) ^{2}}{\frac{45}{2}} = 1

y^{(2)} - x^{(2)} = 100

4 x^{2} - 9 y^{2} - 36 y = 72

3 x^{2} + 2 x - 3 y^{2} + 14 y = - 24

What is 4y^2-24y-2x^2+20=2 ?
The solution to 4y^2-24y-2x^2+20=2 is Hyperbola with (h,k)=(0,3),a= 3/(sqrt(2)),b=3