What is 50x^2-4y^2-200x+24y+36=0 ?

The solution to 50x^2-4y^2-200x+24y+36=0 is Hyperbola with (h,k)=(2,3),a= 8/5 ,b=4sqrt(2)

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50x^2-4y^2-200x+24y+36=0

50 x^{2} - 4 y^{2} - 200 x + 24 y + 36 = 0

(h, k) = (2, 3), a = \frac{8}{5}, b = 42

Solution steps

50 x^{2} - 4 y^{2} - 200 x + 24 y + 36 = 0

Rewrite

50 x^{2} - 4 y^{2} - 200 x + 24 y + 36 = 0

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{( \frac{8}{5} ) ^{2}} - \frac{( y - 3 ) ^{2}}{( 4 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 3), a = \frac{8}{5}, b = 42

\frac{( x - 4 ) ^{2}}{9} - \frac{( y - 2 ) ^{2}}{4} = 1

a^{2} - b^{2} = 31

9 y^{2} - 25 x^{2} + 54 y + 150 x = 369

y^{2} = 8^{2} + x^{2}

a^{2} - b^{2} = - 5

What is 50x^2-4y^2-200x+24y+36=0 ?
The solution to 50x^2-4y^2-200x+24y+36=0 is Hyperbola with (h,k)=(2,3),a= 8/5 ,b=4sqrt(2)