What is y^2=4x^2+25 ?

The solution to y^2=4x^2+25 is Hyperbola with (h,k)=(0,0),a=5,b= 5/2

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y^2=4x^2+25

y^{2} = 4 x^{2} + 25

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

Solution steps

y^{2} = 4 x^{2} + 25

Rewrite

y^{2} = 4 x^{2} + 25

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

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

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

3 x^{(2)} - 6 x - 4 y^{(2)} - 9 = 0

x^{2} - 3 y^{2} - 6 x + 12 = 0

\frac{- y ^{2}}{4} + \frac{z ^{2}}{4} = - \frac{3}{4}

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