What is (y^2}{27}-\frac{x^2)/9 =1 ?

The solution to (y^2}{27}-\frac{x^2)/9 =1 is Hyperbola with (h,k)=(0,0),a=3sqrt(3),b=3

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(y^2}{27}-\frac{x^2)/9 =1

\frac{y ^{2}}{27} - \frac{x ^{2}}{9} = 1

(h, k) = (0, 0), a = 33, b = 3

Solution steps

\frac{y ^{2}}{27} - \frac{x ^{2}}{9} = 1

Rewrite

\frac{y ^{2}}{27} - \frac{x ^{2}}{9} = 1

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 33, b = 3

\frac{( y - 2 ) ^{2}}{16} - \frac{( x - 1 ) ^{2}}{9} = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 2 ) ^{2}}{9} = 1

2 x^{2} - 3 y^{2} = 9

\frac{x ^{2}}{25} - \frac{y ^{2}}{100} = 1

d^{2} = (3 - 20 t)^{2} + (4 - 30 t)^{2}

What is (y^2}{27}-\frac{x^2)/9 =1 ?
The solution to (y^2}{27}-\frac{x^2)/9 =1 is Hyperbola with (h,k)=(0,0),a=3sqrt(3),b=3