What is 4x^2-25y^2+24x+100y+36=0 ?

The solution to 4x^2-25y^2+24x+100y+36=0 is Hyperbola with (h,k)=(-3,2),a=2,b=5

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4x^2-25y^2+24x+100y+36=0

4 x^{2} - 25 y^{2} + 24 x + 100 y + 36 = 0

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

Solution steps

4 x^{2} - 25 y^{2} + 24 x + 100 y + 36 = 0

Rewrite

4 x^{2} - 25 y^{2} + 24 x + 100 y + 36 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

16 x^{2} - 4 y^{2} = 49

16 x^{2} - 9 y^{2} - 36 y = 108

x^{2} + y^{2} - 8 x^{2} + 7 = 0

16 x^{2} - 4 y^{2} = 64

(24 - x^{2}) + (4 - y)^{2} = \frac{x ^{2} + ( y + 3 ) ^{2}}{2 3 ^{2}}

What is 4x^2-25y^2+24x+100y+36=0 ?
The solution to 4x^2-25y^2+24x+100y+36=0 is Hyperbola with (h,k)=(-3,2),a=2,b=5