What is 100^2+15t^2=d^2 ?

The solution to 100^2+15t^2=d^2 is Hyperbola with (h,k)=(0,0),a=100,b=(20sqrt(5))/(sqrt(3))

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100^2+15t^2=d^2

10 0^{2} + 15 t^{2} = d^{2}

(h, k) = (0, 0), a = 100, b = \frac{20 5}{3}

Solution steps

10 0^{2} + 15 t^{2} = d^{2}

Rewrite

10 0^{2} + 15 t^{2} = d^{2}

in the form of a standard hyperbola equation

\frac{( d - 0 ) ^{2}}{10 0 ^{2}} - \frac{( t - 0 ) ^{2}}{( \frac{20 5}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 100, b = \frac{20 5}{3}

x^{2} - y^{2} - 6 x - 2 y - 10 = 0

y^{2} = x^{2} - 8 x

X^{2} - 81 Y^{2} = 81

25 x^{2} - y^{2} - 150 x + 200 = 0

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

What is 100^2+15t^2=d^2 ?
The solution to 100^2+15t^2=d^2 is Hyperbola with (h,k)=(0,0),a=100,b=(20sqrt(5))/(sqrt(3))