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

# Find The Locus Of A Point That Divides A Chord Of Slope 2 Of The Parabola y2= 4x internally In The Ratio 1: 2.

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## Question

### Solution

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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