What is 4x^2=y^2+100 ?

The solution to 4x^2=y^2+100 is Hyperbola with (h,k)=(0,0),a=5,b=10

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4x^2=y^2+100

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

(h, k) = (0, 0), a = 5, b = 10

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 5, b = 10

\frac{x ^{2}}{1} - \frac{y ^{2}}{35} = 1

\frac{( x - 1 ) ^{2}}{3} - \frac{y ^{2}}{4} = 1

x^{2} - y^{2} - 64 = 0

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

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

What is 4x^2=y^2+100 ?
The solution to 4x^2=y^2+100 is Hyperbola with (h,k)=(0,0),a=5,b=10