What is 4x^2+16x-25y^2+50y-109=0 ?

The solution to 4x^2+16x-25y^2+50y-109=0 is Hyperbola with (h,k)=(-2,1),a=5,b=2

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4x^2+16x-25y^2+50y-109=0

4 x^{2} + 16 x - 25 y^{2} + 50 y - 109 = 0

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

Solution steps

4 x^{2} + 16 x - 25 y^{2} + 50 y - 109 = 0

Rewrite

4 x^{2} + 16 x - 25 y^{2} + 50 y - 109 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{36} - \frac{x ^{2}}{14} = 1

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

4 x^{2} - y^{2} + 16 x + 16 y - 9 = 0

36 x^{2} - y^{2} - 24 x + 6 y - 41 = 0

What is 4x^2+16x-25y^2+50y-109=0 ?
The solution to 4x^2+16x-25y^2+50y-109=0 is Hyperbola with (h,k)=(-2,1),a=5,b=2