﻿ The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix : Kaysons Education

# The Locus Of The Mid-point Of The Line Segment Joining The Focus To A Moving Point On The Parabola y2 = 4ax is Another Parabola With Directrix

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## Question

### Solution

Correct option is

x = 0

y2 = 4ax              … (1)

Its focus is S(a, 0). Any point on (1) is P (t12, 2t1).

Let M(x, y) be mid-point of chord PS, then

… (2)

… (3)

Eliminating t between (2) and (3).

Take

Its directrix is X = –A  .

#### SIMILAR QUESTIONS

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