What is 4x^2-24x-25y^2+250y-489=0 ?

The solution to 4x^2-24x-25y^2+250y-489=0 is Hyperbola with (h,k)=(3,5),a=2,b=5

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4x^2-24x-25y^2+250y-489=0

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

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

Solution steps

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

Rewrite

4 x^{2} - 24 x - 25 y^{2} + 250 y - 489 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

4 x^{2} - y^{2} + 24 x + 40 = 0

4 x^{2} - y^{2} + 16 x + 2 y = 21

9 x^{2} - 4 y^{2} + 36 x + 40 y - 208 = 0

x^{2} - 5 y^{2} + 10 y + 4 x - 37 = 0

What is 4x^2-24x-25y^2+250y-489=0 ?
The solution to 4x^2-24x-25y^2+250y-489=0 is Hyperbola with (h,k)=(3,5),a=2,b=5