What is x^2-4y^2+6x+24y-40=0 ?

The solution to x^2-4y^2+6x+24y-40=0 is Hyperbola with (h,k)=(-3,3),a=sqrt(13),b=(sqrt(13))/2

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x^2-4y^2+6x+24y-40=0

x^{2} - 4 y^{2} + 6 x + 24 y - 40 = 0

(h, k) = (- 3, 3), a = 13, b = \frac{13}{2}

Solution steps

x^{2} - 4 y^{2} + 6 x + 24 y - 40 = 0

Rewrite

x^{2} - 4 y^{2} + 6 x + 24 y - 40 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 3 ) ) ^{2}}{( 13 ) ^{2}} - \frac{( y - 3 ) ^{2}}{( \frac{13}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, 3), a = 13, b = \frac{13}{2}

\frac{( y - 1 ) ^{2}}{9} - \frac{( x + 2 ) ^{2}}{16} = 1

x^{2} - 9 y^{2} = 27

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

4 x^{2} = y^{2} + 100

\frac{x ^{2}}{1} - \frac{y ^{2}}{35} = 1

What is x^2-4y^2+6x+24y-40=0 ?
The solution to x^2-4y^2+6x+24y-40=0 is Hyperbola with (h,k)=(-3,3),a=sqrt(13),b=(sqrt(13))/2