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## Homework Statement

The triangle formed by the tangents to the parabola y

^{2}=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

## Homework Equations

## 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=√a

^{2}=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?