What is 25y^2-x^2+2x+150y+225=0 ?

The solution to 25y^2-x^2+2x+150y+225=0 is Hyperbola with (h,k)=(1,-3),a=1,b= 1/5

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25y^2-x^2+2x+150y+225=0

25 y^{2} - x^{2} + 2 x + 150 y + 225 = 0

(h, k) = (1, - 3), a = 1, b = \frac{1}{5}

Solution steps

25 y^{2} - x^{2} + 2 x + 150 y + 225 = 0

Rewrite

25 y^{2} - x^{2} + 2 x + 150 y + 225 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, - 3), a = 1, b = \frac{1}{5}

\frac{( y + 5 ) ^{2}}{9} - \frac{( x - 3 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{16} = 1

x^{2} - y^{2} = \frac{64}{5}

y^{2} = x^{2} - 5 x + 4

a^{2} - b^{2} = 50

What is 25y^2-x^2+2x+150y+225=0 ?
The solution to 25y^2-x^2+2x+150y+225=0 is Hyperbola with (h,k)=(1,-3),a=1,b= 1/5