the lengths of the perpendiculars from the focus and the extremities of a focal chord of a parabola on the tangent at the vertex form

1. an AP
2. a GP
3. an HP
4. none of these

Answer is 3 HP

Let one coordinate of focal chord is P(at², 2at)
So ohter cordinate will be Q(a/t²,-2a/t)
Also S(a,0) is the focus

Now PS=PM=l₁ and QS=QM=l₂
Now l₁= distance from directrix = a + at²
Now l₁= distance from directrix = a + a/t²

Now find out
this will come equal to ‘a‘(semi-major axis)

#its an important result you can remember also.