Question
The lines joining the points of intersection of line x + y = 1 and curve x2+y2−2y+λ=0 to the origin are perpendicular, then the value of λ will be
Answer: Option D
:
D
Making the equation of curve homogeneous with the help of line x + y =1,we get
x2+y2−2y(x+y)+λ(x+y)2=0
⇒x2(1+λ)+y2(−1+λ)−2yx=0
Therefore the lines be perpendicular, if A +B = 0.
⇒1+λ−1+λ=0⇒λ=0
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:
D
Making the equation of curve homogeneous with the help of line x + y =1,we get
x2+y2−2y(x+y)+λ(x+y)2=0
⇒x2(1+λ)+y2(−1+λ)−2yx=0
Therefore the lines be perpendicular, if A +B = 0.
⇒1+λ−1+λ=0⇒λ=0
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