Triangle formed by tangents to a parabola

[takando12]

Homework Statement

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

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=√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?

 

[Samy_A]

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

 

[Ganishk]

Homework Statement

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

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=√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?

Since x = √a² Clearly a is not equal to +a therefore the the abcissa is -a.
And the option three is correct

 

[LCKurtz]

Have you noticed you are replying to a post that was made almost 3 years ago?