What is 9x^2-25y^2=1 ?

The solution to 9x^2-25y^2=1 is Hyperbola with (h,k)=(0,0),a= 1/3 ,b= 1/5

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9x^2-25y^2=1

9 x^{2} - 25 y^{2} = 1

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{5}

Solution steps

9 x^{2} - 25 y^{2} = 1

Rewrite

9 x^{2} - 25 y^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{3}, b = \frac{1}{5}

(x + 3)^{2} - (y + 2)^{2} = 3

9 x^{2} - 4 y^{2} - 54 x + 17 y - 20 = 0

\frac{x ^{2}}{729} - \frac{y ^{2}}{484} = 1

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

5 x^{2} - 4 y^{2} - 20 x - 8 y = 4

What is 9x^2-25y^2=1 ?
The solution to 9x^2-25y^2=1 is Hyperbola with (h,k)=(0,0),a= 1/3 ,b= 1/5