What is 7x^2-24y^2=41 ?

The solution to 7x^2-24y^2=41 is Hyperbola with (h,k)=(0,0),a=sqrt(41/7),b=(sqrt(41))/(2sqrt(6))

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7x^2-24y^2=41

7 x^{2} - 24 y^{2} = 41

(h, k) = (0, 0), a = \frac{41}{7}, b = \frac{41}{2 6}

Solution steps

7 x^{2} - 24 y^{2} = 41

Rewrite

7 x^{2} - 24 y^{2} = 41

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{41}{7} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{41}{2 6} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{41}{7}, b = \frac{41}{2 6}

9 y^{2} - 4 x^{2} - 36 y - 8 x = 4

- x^{2} + y^{2} - 8 y - 9 = 0

\frac{2 x ^{2}}{25} - \frac{( y - 3 ) ^{2}}{49} = 1

9 x^{2} - y^{2} - 54 x + 45 = 0

3 y^{2} - 4 x^{2} - 6 y - 24 x - 105 = 0

What is 7x^2-24y^2=41 ?
The solution to 7x^2-24y^2=41 is Hyperbola with (h,k)=(0,0),a=sqrt(41/7),b=(sqrt(41))/(2sqrt(6))