What is y^2-4x^2+8x=20y+4 ?

The solution to y^2-4x^2+8x=20y+4 is Hyperbola with (h,k)=(1,10),a=10,b=5

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y^2-4x^2+8x=20y+4

y^{2} - 4 x^{2} + 8 x = 20 y + 4

(h, k) = (1, 10), a = 10, b = 5

Solution steps

y^{2} - 4 x^{2} + 8 x = 20 y + 4

Rewrite

y^{2} - 4 x^{2} + 8 x = 20 y + 4

in the form of a standard hyperbola equation

\frac{( y - 10 ) ^{2}}{1 0 ^{2}} - \frac{( x - 1 ) ^{2}}{5 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (1, 10), a = 10, b = 5

\frac{x ^{2}}{4} - \frac{y ^{2}}{32} = 1

16 x^{2} - 9 y^{2} - 32 x + 36 y + 124 = 0

4 y^{2} - 3 x^{2} - 8 y + 6 x - 3 = 0

- x^{2} + 9 y^{2} + 90 y + 189 = 0

\frac{( x ^{2} )}{625} - \frac{( y ^{2} )}{3600} = 1

What is y^2-4x^2+8x=20y+4 ?
The solution to y^2-4x^2+8x=20y+4 is Hyperbola with (h,k)=(1,10),a=10,b=5