﻿ Find the locus of the mid-points of the chord of the parabola y2 = 4ax which subtend a right angle at the vertex. : Kaysons Education

# Find The Locus Of The Mid-points Of The Chord Of The Parabola y2 = 4ax which Subtend A Right Angle At The Vertex.

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## Question

### Solution

Correct option is

y2 = 2a(– 4a).

Let P be t1 and Q be t2 and since PQ subtends a right angle at the vertex O(0, 0) therefore as in t­1 t­2 = – 4. If (h, k) be the mid-point, then 2h = (t12 + t22) and 2k = 2a(t1 + t2)

or   2h = a[(t1 + t2)2 – 2t1t2]

or

Locus is y2 = 2a(– 4a).

#### SIMILAR QUESTIONS

Q1

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Q2

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Q3

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Q4

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Q6

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