What is (y^2)/(a^2)-(x^2)/(b^2)=1 ?

The solution to (y^2)/(a^2)-(x^2)/(b^2)=1 is Hyperbola with (h,k)=(0,0),a=a,b=b

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(y^2)/(a^2)-(x^2)/(b^2)=1

\frac{y ^{2}}{a ^{2}} - \frac{x ^{2}}{b ^{2}} = 1

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

Solution steps

\frac{y ^{2}}{a ^{2}} - \frac{x ^{2}}{b ^{2}} = 1

Rewrite

\frac{y ^{2}}{a ^{2}} - \frac{x ^{2}}{b ^{2}} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

\frac{( y - 5 ) ^{2}}{25} - \frac{( x + 5 ) ^{2}}{9} = 1

4 x^{2} - 9 y^{2} + 4 x + 36 y - 36 = 0

9 x^{2} - 16 y^{2} - 36 x + 96 y - 252 = 0

\frac{x ^{2} - 8 x + 16}{16} - \frac{y ^{2} + 4 y - 4}{9} = 0

50 x^{2} - 25 y^{2} + 144 x - 68 y - 75 = 0

What is (y^2)/(a^2)-(x^2)/(b^2)=1 ?
The solution to (y^2)/(a^2)-(x^2)/(b^2)=1 is Hyperbola with (h,k)=(0,0),a=a,b=b