Find the locus of a point that divides a chord of slope 2 of the parabola y2= 4x internally in the ratio 1: 2.


Correct option is

4x = 9y2 – 12y + 8

 be the end points of chord AB.  

Also let M ≡ (x1y1) be a point which divides AB internally in ratio 1: 2.

It is given that slope of PQ = 2.  



As M divides PQ in 1 : 2 ratio, we get:  



we have t eliminate two variables t1 and t2 between (i), (ii) and (iii).

From (i), put t2 = 1 – tin (iii) to get:  


On substituting the values of t1 and t2 in (ii), we get:  


Replacing x1 by x and y, we get the required locus as:  

             4x = 9y2 – 12y + 8  



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