(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
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