What is 25x^2-y^2+50x+6y-9=0 ?

The solution to 25x^2-y^2+50x+6y-9=0 is Hyperbola with (h,k)=(-1,3),a=1,b=5

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25x^2-y^2+50x+6y-9=0

25 x^{2} - y^{2} + 50 x + 6 y - 9 = 0

(h, k) = (- 1, 3), a = 1, b = 5

Solution steps

25 x^{2} - y^{2} + 50 x + 6 y - 9 = 0

Rewrite

25 x^{2} - y^{2} + 50 x + 6 y - 9 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 1, 3), a = 1, b = 5

\frac{( x + 1 ) ^{2}}{4} - \frac{( y + 2 ) ^{2}}{9} = 1

x^{2} - y^{2} - 1 < 0

\frac{y ^{2}}{9} - \frac{x ^{2}}{1} = 1

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

\frac{( x + 4 ) ^{2}}{9} - \frac{( y - 3 ) ^{2}}{25} = 1

What is 25x^2-y^2+50x+6y-9=0 ?
The solution to 25x^2-y^2+50x+6y-9=0 is Hyperbola with (h,k)=(-1,3),a=1,b=5