What is 16y^2-9x^2+90x-64y-305=0 ?

The solution to 16y^2-9x^2+90x-64y-305=0 is Hyperbola with (h,k)=(5,2),a=3,b=4

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16y^2-9x^2+90x-64y-305=0

16 y^{2} - 9 x^{2} + 90 x - 64 y - 305 = 0

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

Solution steps

16 y^{2} - 9 x^{2} + 90 x - 64 y - 305 = 0

Rewrite

16 y^{2} - 9 x^{2} + 90 x - 64 y - 305 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{x ^{2}}{12} - \frac{y ^{2}}{4} = 1

\frac{( x + 2 ) ^{2}}{16} - \frac{( y - 3 ) ^{2}}{25} = 1

x^{2} - y^{2} + 6 x + 2 y = 6

3 x^{2} - y^{2} + 18 x + 8 y + 38 = 0

0 = 1 + y^{2} - x^{2}

What is 16y^2-9x^2+90x-64y-305=0 ?
The solution to 16y^2-9x^2+90x-64y-305=0 is Hyperbola with (h,k)=(5,2),a=3,b=4