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

- y^{2} + x^{2} + 26 y - 26 x = - 121

(y + 2)^{2} - 25 (x - 2)^{2} = 25

x, x^{2} - x + 1 - 2 k (x)^{2} + 4 k + 1 = 0

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

- 2 x^{2} + 4 y^{2} - 3 x - 43 y + 44 = 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