1. ## Parabola!!

Hey anyone got any ideas on how to solve this??
Right I have done the first part: Is it possible for the tangents to a parabola at two distinct zeroes (x intercepts) to meet at right angles?
But need help on:
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?

Thanks!! xx

2. Originally Posted by jessismith
Hey anyone got any ideas on how to solve this??
Right I have done the first part: Is it possible for the tangents to a parabola at two distinct zeroes (x intercepts) to meet at right angles?
But need help on:
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?

Thanks!! xx
Do you have a classmate named Sonia? Because she asked the same questions in a previous thread (in the third post), and some answers were given, but only on the part you did...

3. Yep I did search which gave me the answer to the first part (like stated in question) but the other questions were not answered. :-)

4. Hello, jessismith

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?
Here's a bit of parabolic trivia . . .

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 . . .
Code:
|
*      |      *
|
* A   |F  B *
---o----+----o-----
\*  |  */
\  *  /
\ | /
\|/
- - - - o - - - - -
|C

Then the intercepts at $A$ and $B$ have tangents so that $AC \perp BC.$