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

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

\frac{( y + 3 ) ^{2}}{9} - \frac{x ^{2}}{16} = 1

x^{2} - 6 = \frac{y ^{2}}{3}

12 (y - 5)^{2} - 30 (x + 2)^{2} = 360

3 x^{2} - y^{2} + 30 x + 78 = 0

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)