What is (3r^2)/(t+2)>= 5t ?

The solution to (3r^2)/(t+2)>= 5t is Hyperbola with (h,k)=(0,-1),a=1,b=sqrt(5/3)

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(3r^2)/(t+2)>= 5t

\frac{3 r ^{2}}{t + 2} \geq 5 t

(h, k) = (0, - 1), a = 1, b = \frac{5}{3}

Solution steps

\frac{3 r ^{2}}{t + 2} \geq 5 t

Rewrite

\frac{3 r ^{2}}{t + 2} - 5 t \geq 0

in the form of a standard hyperbola equation

\frac{( t - ( - 1 ) ) ^{2}}{1 ^{2}} - \frac{( r - 0 ) ^{2}}{( \frac{5}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - 1), a = 1, b = \frac{5}{3}

36 x^{2} - 25 y^{2} = 900

2 x 6 x - y 4 y = 6 - 10

3 x^{2} - y^{2} + 6 x = 0

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

9 x^{2} - 4 y^{2} + 18 x - 16 y - 43 = 0

What is (3r^2)/(t+2)>= 5t ?
The solution to (3r^2)/(t+2)>= 5t is Hyperbola with (h,k)=(0,-1),a=1,b=sqrt(5/3)