Straight LineEasy
Question
If 
= λx + iμy, then locus of P(x, y) will represents a/an :-
= λx + iμy, then locus of P(x, y) will represents a/an :-Options
A.Ellipse if λ = 1, μ = 2
B.Pair of straight line if λ = 1, μ = 0
C.Circle, if λ = 1, μ = 1
D.All of them
Solution
- 2 = eiθ 
= eiθtaking modulus both side
(3 - 2λx)2 + 4μ2y2 = λ2x2 + μ2y2
3λ2x2 + 3μ2y2 - 12λx + 9 = 0
at λ = 1, μ = 2
3x2 - 12x + 12y2 + 9 = 0
3(x2 - 4x + 4) + 12y2 + 9 - 12 = 0
3(x - 2)2 + 12y2 = 3
= 1 rep-ellipseat λ = 1, μ = 1 rep. circle
at λ =1, μ = 0
3x2 - 12x + 9 = 0 rep pair of straight lines
x2 - 4x + 3 = 0
(x - 1) (x - 3) = 0; x = 1, x = 3
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