Here's a bit of parabolic trivia . . . Is it possible for the tangents to a parabola at two distinct zeroes
to meet at right angles?
Is it possible to find such a parabola for which the x and y intercepts
and the point of intersection of the two tangents lie on the integer lattice?
What can you say about cubics?
The endpoints of a focal chord (a chord through the focus) have tangents
. . which are perpendicular and intersect on the directrix.
So if we place the focus at the origin . . .
* | *
* A |F B *
\* | */
\ * /
\ | /
- - - - o - - - - -
Then the intercepts at and have tangents so that