The lines joining the points of intersection of line x - y - 1 and curve x-2 - y-2 - 2y - - - 0 to the origin are perpendicular- then the value of - will be nbsp- 1-2-0-1-2-

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Homogenization

The lines joi...

Question

The lines joining the points of intersection of line x + y = 1 and curve $x^{2} + y^{2} - 2 y + λ = 0$ to the origin are perpendicular, then the value of $λ$ will be

1/2

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Solution

The correct option is D
0

Making the equation of curve homogeneous with the help of line x + y =1,we get

$x^{2} + y^{2} - 2 y (x + y) + λ (x + y)^{2} = 0$

$\Rightarrow x^{2} (1 + λ) + y^{2} (- 1 + λ) - 2 y x = 0$

Therefore the lines be perpendicular, if A + B = 0.

$\Rightarrow 1 + λ - 1 + λ = 0 \Rightarrow λ = 0$

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