What is -4x^2+4y^2-24x+32y=-24 ?

The solution to -4x^2+4y^2-24x+32y=-24 is Hyperbola with (h,k)=(-3,-4),a=1,b=1

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-4x^2+4y^2-24x+32y=-24

- 4 x^{2} + 4 y^{2} - 24 x + 32 y = - 24

(h, k) = (- 3, - 4), a = 1, b = 1

Solution steps

- 4 x^{2} + 4 y^{2} - 24 x + 32 y = - 24

Rewrite

- 4 x^{2} + 4 y^{2} - 24 x + 32 y = - 24

in the form of a standard hyperbola equation

\frac{( y - ( - 4 ) ) ^{2}}{1 ^{2}} - \frac{( x - ( - 3 ) ) ^{2}}{1 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 3, - 4), a = 1, b = 1

8 x^{2} - 15 y^{2} = 24

4 x^{2} - 9 y^{2} - 8 x + 36 y + 4 = 0

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

x^{2} - 4 y^{2} = 25

x^{2} - 4 y^{2} = 37

What is -4x^2+4y^2-24x+32y=-24 ?
The solution to -4x^2+4y^2-24x+32y=-24 is Hyperbola with (h,k)=(-3,-4),a=1,b=1