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Question

(2 + 2λ + μ)x2 + (1 + 2λ + 2μ)y2 + (3 + 5λ + 3μ)xy

(16 + 14λ + 11μ)x (10 + 13λ + 17μ) + (24 + 20λ + 30μ) = 0 is an equation of circle only when


A

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B

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C

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D

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Solution

The correct option is D


If given equation:

(2 + 2λ + μ)x2 + (1 + 2λ + 2μ)y2 + (3 + 5λ + 3μ )xy

(16 + 14λ + 11μ)x (10 + 13λ + 17μ) + (24 + 20λ + 30μ) = 0 is an equation of circle.

Then coefficient of x2 = coefficient of y2

2 + 2λ +μ = 1 + 2λ + 2μ

μ = 1

And coefficient of xy = 0

3 + 5λ + 3μ = 0

Substituting μ = 1

3 + 5λ + 3 = 0

λ =65

So, option D is correct


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