# Homework Help: Triangle formed by tangents to parabola.

1. Dec 10, 2015

### takando12

1. The problem statement, all variables and given/known data
The triangle formed by the tangents to the parabola y2=4ax, at the ends of the latus rectum and the double ordinate through it's focus is:
1) equilateral 2) acute angles isosceles 3)right angled isosceles 4) dependent on value of a

2. Relevant equations

3. The attempt at a solution
The double ordinate through the focus is the latus rectum. I tried to find the intersection of the two tangents by using the AM and GM of the co-ordinates of the points of contact with the parabola .
the two points of contact : (a,2a) and (a,-2a)
x-coordinate of intersection = GM=√a2=a
y-coordinate of intersection = AM= 2a-2a/2 =0
Which gives me the intersection of the two tangents to be (a,0) which is the co-ordinates of the focus. This is clearly wrong. Where am I going wrong in my approach?

2. Dec 10, 2015

### Samy_A

Maybe you should post how you compute(d) the slope of the tangents at the two points of contact.