ParabolaHard
Question
PQ is a normal chord of the parabola y2 = 4ax at P, A being the vertex of the parabola. Through P a line is drawn parallel to AQ meeting the x-axis in R. Then the length of of AR is -
Options
A.equal to the length of the latus rectum
B.equal to the focal distance of the point P.
C.equal to twice the focal distance of the point P.
D.equal to the distance of the point P from the directrix
Solution
et P (at12, 2at1)
Relation between t1 & t2
t2 = - t1 - 2/t1
equation of line PR
y - 2at1 =
(x - at12)Put y = 0 and t2 = - t1 -
, we getR = ((-at1 t2 + at 12), 0)
R = (2a(1 + t12), 0)
Length of PS = a(1 + t12)
So AR is twice of PS.
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