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

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

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4y^2=x^2+100

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

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

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{y ^{2}}{64} - \frac{x ^{2}}{49} = 1

\frac{( x - 4 ) ^{2}}{9} - \frac{( y + 7 ) ^{2}}{81} = 1

\frac{y ^{2}}{49} - \frac{x ^{2}}{16} = 1

9 y^{2} - 7 x^{2} = 63

0 = x^{2} - y^{2} + 1

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