What is 25x^2-4y^2+40y=0 ?

The solution to 25x^2-4y^2+40y=0 is Hyperbola with (h,k)=(0,5),a=5,b=2

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25x^2-4y^2+40y=0

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

(h, k) = (0, 5), a = 5, b = 2

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( y - 5 ) ^{2}}{5 ^{2}} - \frac{( x - 0 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 5), a = 5, b = 2

5 y^{2} - 4 x^{2} - 80 = 0

(u - 7)^{2} = 2 y^{2} - 18 y + 28

2 (x^{2} - 10 x) - 9 (y^{2} - 8 y) = - 16

\frac{x ^{2}}{36} - \frac{y ^{2}}{100} = 1

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

What is 25x^2-4y^2+40y=0 ?
The solution to 25x^2-4y^2+40y=0 is Hyperbola with (h,k)=(0,5),a=5,b=2