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

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

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

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

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

Solution steps

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

Rewrite

4 x^{2} - 25 y^{2} + 16 x + 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

x^{2} + 12 = y^{2} + 6 x - 2 y

- 36 x^{2} + 25 y^{2} = 900

\frac{y ^{2}}{12} - \frac{x ^{2}}{4} = 1

\frac{16 y ^{2}}{1} - \frac{25 x ^{2}}{1} = 1

- 9 x^{2} + 25 y^{2} - 72 x - 144 - 100 y = 0

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