What is 25x^2-4y^2+50x+8y+121=0 ?

The solution to 25x^2-4y^2+50x+8y+121=0 is Hyperbola with (h,k)=(-1,1),a=5,b=2

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25x^2-4y^2+50x+8y+121=0

25 x^{2} - 4 y^{2} + 50 x + 8 y + 121 = 0

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

Solution steps

25 x^{2} - 4 y^{2} + 50 x + 8 y + 121 = 0

Rewrite

25 x^{2} - 4 y^{2} + 50 x + 8 y + 121 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - y^{2} = 12

x^{2} - y^{2} = 17

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

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

\frac{( x - 7 ) ^{2}}{64} - \frac{( y - 6 ) ^{2}}{36} = 1

What is 25x^2-4y^2+50x+8y+121=0 ?
The solution to 25x^2-4y^2+50x+8y+121=0 is Hyperbola with (h,k)=(-1,1),a=5,b=2