What is 4x^2-5y^2-32x+10y+79=0 ?

The solution to 4x^2-5y^2-32x+10y+79=0 is Hyperbola with (h,k)=(4,1),a=2,b=sqrt(5)

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4x^2-5y^2-32x+10y+79=0

4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

(h, k) = (4, 1), a = 2, b = 5

Solution steps

4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

Rewrite

4 x^{2} - 5 y^{2} - 32 x + 10 y + 79 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (4, 1), a = 2, b = 5

(x + k (x)) (x - k (x)) = k (x)

\frac{x ^{2}}{16} - \frac{y ^{2}}{64} = 1

\frac{x ^{2}}{81} - \frac{y ^{2}}{64} = 1

2 y^{2} - 9 x^{2} - 18 x + 20 y + 5 = 0

36 = 9 x^{2} - 4 y^{2}

What is 4x^2-5y^2-32x+10y+79=0 ?
The solution to 4x^2-5y^2-32x+10y+79=0 is Hyperbola with (h,k)=(4,1),a=2,b=sqrt(5)