What is 2x^2-5y^2=52 ?

The solution to 2x^2-5y^2=52 is Hyperbola with (h,k)=(0,0),a=sqrt(26),b=(2sqrt(13))/(sqrt(5))

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2x^2-5y^2=52

2 x^{2} - 5 y^{2} = 52

(h, k) = (0, 0), a = 26, b = \frac{2 13}{5}

Solution steps

2 x^{2} - 5 y^{2} = 52

Rewrite

2 x^{2} - 5 y^{2} = 52

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 26 ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{2 13}{5} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 26, b = \frac{2 13}{5}

- 4 x^{2} + y^{2} + 20 x + 10 y - 25 = 0

\frac{9 y ^{2}}{36} - \frac{4 x ^{2}}{36} = 1

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

x^{2} + (5 - 6) y^{2} = 1

x^{2} + 11 = y^{2} + 4 x - 2 y

What is 2x^2-5y^2=52 ?
The solution to 2x^2-5y^2=52 is Hyperbola with (h,k)=(0,0),a=sqrt(26),b=(2sqrt(13))/(sqrt(5))