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

The solution to x^2-y^2+8x+24y=0 is Hyperbola with (h,k)=(-4,12),a=8sqrt(2),b=8sqrt(2)

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

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

(h, k) = (- 4, 12), a = 82, b = 82

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 12 ) ^{2}}{( 8 2 ) ^{2}} - \frac{( x - ( - 4 ) ) ^{2}}{( 8 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, 12), a = 82, b = 82

\frac{( x - 9 ) ^{2}}{16} - \frac{( y - 11 ) ^{2}}{9} = 1

- 9 x^{2} + z^{2} = 36

x^{2} - y^{2} = 19

4 x^{2} + 4 x + 1 - 2 y^{2} = 16

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

What is x^2-y^2+8x+24y=0 ?
The solution to x^2-y^2+8x+24y=0 is Hyperbola with (h,k)=(-4,12),a=8sqrt(2),b=8sqrt(2)