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PQ is a normal chord of the parabola y^2...

`PQ` is a normal chord of the parabola `y^2= 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 `AR` is : (A) equal to the length of the latus rectum (B) equal to the focal distance of the point P (C) equal to the twice of the focal distance of the point P (D) equal to the distance of the point P from the directrix.

Text Solution

Verified by Experts

given that `y^2= 4ax`
let the point P be `(at_1^2, 2at_1)`
`t_2= -t_1-2/t_1`
`m_(AQ) = (2at_2-0)/(at_2^2-0) = 2/t_2`
the eqn of the line will be
`y-2at_1= 2/t_2(x-at_1^2)`
put `y=0`
`=> -2at_1= 2/t_2(x-at_1^2)`
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