What is 5x^2=5y^2+45 ?

The solution to 5x^2=5y^2+45 is Hyperbola with (h,k)=(0,0),a=3,b=3

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5x^2=5y^2+45

5 x^{2} = 5 y^{2} + 45

(h, k) = (0, 0), a = 3, b = 3

Solution steps

5 x^{2} = 5 y^{2} + 45

Rewrite

5 x^{2} = 5 y^{2} + 45

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 3, b = 3

- 3 y^{2} - 8 x + 4 x^{2} - 8 = 0

- \frac{y ^{2}}{49} + \frac{x ^{2}}{9} = 1

18 x^{2} = 28 + 8 y^{2}

4 x^{2} - 9 y^{2} - 48 x + 108 = 0

\frac{( x - 9 ) ^{2}}{9} - \frac{( y + 4 ) ^{2}}{25} = 1

What is 5x^2=5y^2+45 ?
The solution to 5x^2=5y^2+45 is Hyperbola with (h,k)=(0,0),a=3,b=3