What is 4x^2-5y^2+32x+30y=1 ?

The solution to 4x^2-5y^2+32x+30y=1 is Hyperbola with (h,k)=(-4,3),a=sqrt(5),b=2

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4x^2-5y^2+32x+30y=1

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

(h, k) = (- 4, 3), a = 5, b = 2

Solution steps

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

Rewrite

4 x^{2} - 5 y^{2} + 32 x + 30 y = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (- 4, 3), a = 5, b = 2

3 y^{2} - 5 x^{2} + 18 y - 40 x - 533 = 0

\frac{( y - 3 ) ^{2}}{9} - \frac{( x + 1 ) ^{2}}{27} = 1

y^{2} - 4 x^{2} - 2 y + 24 x = 51

\frac{( x - 1 ) ^{2}}{36} - \frac{( y + 2 ) ^{2}}{25} = 1

\frac{x ^{2}}{3 0 ^{2}} - \frac{y ^{2}}{4 4 ^{2}} = 1

What is 4x^2-5y^2+32x+30y=1 ?
The solution to 4x^2-5y^2+32x+30y=1 is Hyperbola with (h,k)=(-4,3),a=sqrt(5),b=2