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

Q. Find the equations of the straight lines joining the origin to the points of intersection of the line

x - y = 2

and the curve

5 x^{2} + 12 x y - 8 y^{2} + 8 x - 4 y + 12 = 0

and find the angle between them. Also show that these lines are equally inclined to the axes.

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If the straight lines joining the origin and the point of the intersection of the curve x2+12xy−y2+4x−2y+3=0 and x+ky−1=0 are equally inclined to x-axis then the value of k is

The correct option is B −1x+ky=11=(x+ky)2 Now homogenizing the equation of the curve in order to get the equation of pair of straight lines passsing from origin ∴x2+12xy−y2+(4x−2y)(x+ky)+3(x+ky)2=0 ∵ both the lines are equally inclined ∴ coefficient of xy=0 ⇒12+4k−2+6k=0k=−1

If the straight lines joining the origin and the point of the intersection of the curve $x^{2} + 12 x y - y^{2} + 4 x - 2 y + 3 = 0$ and $x + k y - 1 = 0$ are equally inclined to $x$ -axis then the value of $k$ is