What is 9x^2-4y^2+24<= 0 ?

The solution to 9x^2-4y^2+24<= 0 is Hyperbola with (h,k)=(0,0),a=sqrt(6),b=(2sqrt(2))/(sqrt(3))

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9x^2-4y^2+24<= 0

9 x^{2} - 4 y^{2} + 24 \leq 0

(h, k) = (0, 0), a = 6, b = \frac{2 2}{3}

Solution steps

9 x^{2} - 4 y^{2} + 24 \leq 0

Rewrite

9 x^{2} - 4 y^{2} + 24 \leq 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{2 2}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 6, b = \frac{2 2}{3}

x^{2} - 16 y^{2} = 64

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

4 x^{2} - 625 \cdot y^{2} + 2 \cdot y - 1 = 0

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

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

What is 9x^2-4y^2+24<= 0 ?
The solution to 9x^2-4y^2+24<= 0 is Hyperbola with (h,k)=(0,0),a=sqrt(6),b=(2sqrt(2))/(sqrt(3))