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If the line y =sqrt(3)x cuts the curve x...

If the line `y =sqrt(3)x` cuts the curve `x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=0` at the point `A , B , C ,` then `O AdotO BdotO C` is equal to `(k/(13))(3sqrt(3)-1)` . The value of `k` is______

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CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. A Line through the variable point A(1+k,2k) meets the lines 7x+y-16=0;...

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  2. The incident ray is along the line 24x+7y+5=0. Find the equation of mi...

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  3. If the line y =sqrt(3)x cuts the curve x^3+y^3+3x y+5x^2+3y^2+4x+5y-1=...

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  4. Two equal sides of an isosceles triangle are 7x-y+3=0 and x+y-3=0. Its...

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  5. The area of a parallelogram formed by the lines a x+-b y+-c=0 is

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  6. The vertices, B and C of a triangle ABC lie on the lines 3y=4x and y=...

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  7. If each of the points (x1, 4), (-2,y1) lies on the line joining the po...

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  8. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

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  9. The diagonals of a parallelogram PQRS are along the lines x+3y =4 and ...

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  10. For the straight lines 4x+3y-6 = 0 and 5x+12y+9 = 0, find the equation...

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  11. A straight line segment AB of length 'a' moves with its ends on the ax...

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  12. Find the foot of the perpendicular from the point (2,4) upon x+y=1.

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  13. The lines x+y-1=0,(m-1)x+(m^2-7)y-5=0, and (m-2)x+(2m-5)y=0 are (a)con...

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  14. In Delta ABC , vertex A is (1,2). If the internal angle bisector of an...

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  15. Find the equation of the bisector of the obtuse angle between of the l...

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  16. The line ax+by=1 passes through the point of intertsection of y=x tan ...

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  17. A straight line L is perpendicular to the line 5x-y=1. The aera of the...

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  18. The reflection of the point (4,-13) about the line 5x+y+6=0 is a. (-1,...

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  19. Triangle A B C with A B=13 ,B C=5, and A C=12 slides on the coordinat...

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  20. The line y=(3x)/4 meets the lines x-y+1=0 and 2x-y=5 at A and B respec...

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