What is y^2-25x^2+4y+50x-46=0 ?

The solution to y^2-25x^2+4y+50x-46=0 is Hyperbola with (h,k)=(1,-2),a=5,b=1

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y^2-25x^2+4y+50x-46=0

y^{2} - 25 x^{2} + 4 y + 50 x - 46 = 0

(h, k) = (1, - 2), a = 5, b = 1

Solution steps

y^{2} - 25 x^{2} + 4 y + 50 x - 46 = 0

Rewrite

y^{2} - 25 x^{2} + 4 y + 50 x - 46 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 2), a = 5, b = 1

\frac{y ^{2}}{20} - \frac{x ^{2}}{1} = 1

\frac{( y - 5 ) ^{2}}{16} - (x - 2)^{2} = 1

9 x^{2} - 5 y^{2} + 5 = 0

x^{2} - 9 y^{2} - 27 = 0

7 x^{2} - 9 y^{2} - 14 x + 72 y - 200 = 0

What is y^2-25x^2+4y+50x-46=0 ?
The solution to y^2-25x^2+4y+50x-46=0 is Hyperbola with (h,k)=(1,-2),a=5,b=1