﻿ The locus of the points of intersection of the tangents at the extremities of the chords of the ellipse x2 + 2y2 = 6 which touch the ellipse x2 + 4y2 = 4 is : Kaysons Education

# The Locus Of The Points Of Intersection Of The Tangents At The Extremities Of The Chords Of The Ellipse x2 + 2y2 = 6 Which Touch The Ellipse x2 + 4y2 = 4 Is

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## Question

### Solution

Correct option is

x2 + y2 = 9

We can write x2 + 4y2 = 4 as

(1)

Equation of a tangent to the ellipse (1) is

(2)

Equation of the ellipse x2 + 2y2 = 6 can be written as

(3)

Suppose (1) meets the ellipse (3) at P and Q and the tangents atP and Q to the ellipse (3) intersect at (h, k), then (2) is the chord of contact of (h, k) with respect to the ellipse (3) and thus its equation is

(4)

Since (2) and (4) represents the same line

and the locus of (h, k) is x2 + y2 = 9

#### SIMILAR QUESTIONS

Q1

Consider the two curves C1 : y2 = 4x ; C2 : x2 + y2 – 6x + 1, then

Q2

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Q3

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Q4

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Q5

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Q6

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin is

Q7

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Q8

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Q9

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Q10

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