What is 5x^2-2y^2+10x-12y=23 ?

The solution to 5x^2-2y^2+10x-12y=23 is Hyperbola with (h,k)=(-1,-3),a=sqrt(2),b=sqrt(5)

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5x^2-2y^2+10x-12y=23

5 x^{2} - 2 y^{2} + 10 x - 12 y = 23

(h, k) = (- 1, - 3), a = 2, b = 5

Solution steps

5 x^{2} - 2 y^{2} + 10 x - 12 y = 23

Rewrite

5 x^{2} - 2 y^{2} + 10 x - 12 y = 23

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, - 3), a = 2, b = 5

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

4 x^{2} - 9 y^{2} + 3 x + 18 y + 91 = 0

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

y^{2} + 2 y = 4 x^{2} + 3

10 y^{2} - 9 x^{2} = 80

What is 5x^2-2y^2+10x-12y=23 ?
The solution to 5x^2-2y^2+10x-12y=23 is Hyperbola with (h,k)=(-1,-3),a=sqrt(2),b=sqrt(5)