Answer
$\dfrac{x^2}{10000} +\dfrac{y^2}{10000}-\dfrac{z^2}{260416.67} =1$
Work Step by Step
The equation of a hyperboloid of one sheet with the z-axis and centered at the origin can be expressed as:
$\dfrac{x^2}{a^2} +\dfrac{y^2}{b^2}-\dfrac{z^2}{c^2} =1$
Set $y=0$
Now, $\dfrac{x^2}{a^2} -\dfrac{z^2}{c^2} =1$
Suppose $x=\dfrac{280}{2}; z=500$
So, $\dfrac{(140)^2}{(100)^2} -\dfrac{(500)^2}{c^2} =1 \implies -\dfrac{(500)^2}{c^2}=-0.96$
$\implies c^2=\dfrac{(500)^2}{0.96} \approx 260416.67$
The equation (1) becomes:
$\dfrac{x^2}{10000} +\dfrac{y^2}{10000}-\dfrac{z^2}{260416.67} =1$
