What is 5x^2-4y^2+40x+24y+24=0 ?

The solution to 5x^2-4y^2+40x+24y+24=0 is Hyperbola with (h,k)=(-4,3),a=2,b=sqrt(5)

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5x^2-4y^2+40x+24y+24=0

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

(h, k) = (- 4, 3), a = 2, b = 5

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - ( - 4 ) ) ^{2}}{2 ^{2}} - \frac{( y - 3 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 4, 3), a = 2, b = 5

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

x^{2} - 81 y^{2} = 81

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

4 x^{2} - 12 y^{2} - 24 x + 24 y + 51 = 0

y = \frac{273 x}{340 y} x + \frac{240000}{340}

What is 5x^2-4y^2+40x+24y+24=0 ?
The solution to 5x^2-4y^2+40x+24y+24=0 is Hyperbola with (h,k)=(-4,3),a=2,b=sqrt(5)