Let S be a surface given by the equation:
$$ x^2 - y^2 -z = 0 $$
and P be the point $(1,-1,0)$. Find the two lines contained in S that pass through P.
We're not looking for answers outright (hence the 'homework' tag) but hints towards attacking this problem would be greatly appreciated.
Edit: Thanks for all of your responses so far. We are having trouble understanding how to proceed:
We can produce a parametric representation of all lines passing through $(1,-1,0)$ in $R^2$, and substitute this into the surface:
$$ (1+ta)^2-(-1 + tb)^2 = tc $$
Expanding and reducing this we come to;
$$ t^2a^2 - t^2b^2 + 2ta + 2tb = tc $$ $$ ta^2 - tb^2 + 2a + 2b = c $$
In our notes, our lecturer appears to jump from this to
$$ 2a + 2b -c = a^2 - b^2 = 0 $$
Confusing as we have assumed $t=1$ and we have equated to 0, with no real explanation given. How is this done?