﻿ Find the locus of middle point of chord y2 = 4ax drawn through vertex. : Kaysons Education

# Find The Locus Of Middle Point Of Chord y2 = 4ax drawn Through Vertex.

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## Question

### Solution

Correct option is

y2 = 2ax

Let mid-point of the chord be (h, k) then equation of chord in mid-point from is

ky – 2a(x + h) = k2 – 4ah

As all these chords pass through the vertex hence it must satisfy (0, 0)

0 – 2i(0 + h) = k2 – 4ah

4ah – 2ah = k2

k2 = 2ah

Thus required locus is a parabola y2 = 2ax.

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