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Length of the focal chord of the parabola y^2 = 4ax at a distance p from the vertex is?? I NEED THE PROCEDURE OF SOLVING

Length of the focal chord of the parabola y^2 = 4ax at a distance p from the vertex is??
I NEED THE PROCEDURE OF SOLVING

Grade:12

2 Answers

k sesi preetam
7 Points
7 years ago

First consider the points on the parabola where the chord intersects in the parametric form as (at1^2 , 2at1) and (at2^2 , 2at2). As it is a focal chord, t1* t2 = -1. Let this be our first equation. Now consider the equation of chord as we know two points. Now using the formula for the distance of a point from a line ( In this case the point is the origin and the line is the chord)we can get a relation between t1 , t2 , and p. Let this be our second equation. Using these both equations we can get the points which we assumed before in terms of p and then use the distance formula to find the length of the chord. This is how u solve this problem.

Its better to revise your basics on parabolas and even the previous topics as much as possible and know how to use them so that co- ordinate geometry wouldn''t be a big problem.

Ragini
19 Points
3 years ago
For a parabola,
which has a equation ,y2=4ax
focal distancebetween two points =[(x-a)2+y2]1/2
                          =[x2+a2-2ax+y2]½
                   =|x+a|

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