What is 4y^2-24y-2x^2+20x=22 ?

The solution to 4y^2-24y-2x^2+20x=22 is Hyperbola with (h,k)=(5,3),a=sqrt(2),b=2

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

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

(h, k) = (5, 3), a = 2, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 3 ) ^{2}}{( 2 ) ^{2}} - \frac{( x - 5 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, 3), a = 2, b = 2

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

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

9 + x^{2} - 3 y^{2} = 0

- 3 x^{2} + 2 y^{2} + 6 x - 7 y = 7

16 x^{2} - 9 y^{2} + 32 x + 72 y - 704 = 0

What is 4y^2-24y-2x^2+20x=22 ?
The solution to 4y^2-24y-2x^2+20x=22 is Hyperbola with (h,k)=(5,3),a=sqrt(2),b=2