What is 4x^2-5y^2+8x-10y+19=0 ?

The solution to 4x^2-5y^2+8x-10y+19=0 is Hyperbola with (h,k)=(-1,-1),a=2,b=sqrt(5)

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4x^2-5y^2+8x-10y+19=0

4 x^{2} - 5 y^{2} + 8 x - 10 y + 19 = 0

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

Solution steps

4 x^{2} - 5 y^{2} + 8 x - 10 y + 19 = 0

Rewrite

4 x^{2} - 5 y^{2} + 8 x - 10 y + 19 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 y^{2} - 9 x^{2} - 112 y + 36 x + 124 = 0

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

\frac{( x - 6 ) ^{2}}{25} - (y + 1)^{2} = 1

\frac{( y - 6 ) ^{2}}{9} - (x - 6)^{2} = 1

\frac{( x + 2 ) ^{2}}{16} - \frac{y ^{2}}{9} = 1

What is 4x^2-5y^2+8x-10y+19=0 ?
The solution to 4x^2-5y^2+8x-10y+19=0 is Hyperbola with (h,k)=(-1,-1),a=2,b=sqrt(5)