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Consider two lines L1a n dL2 given by a...

Consider two lines `L_1a n dL_2` given by `a_1x+b_1y+c_1=0a n da_2x+b_2y+c_2=0 respectively where c1 and c2 !=0,` intersecting at point `PdotA` line `L_3` is drawn through the origin meeting the lines `L_1a n dL_2` at `Aa n dB ,` respectively, such that `PA=P B` . Similarly, one more line `L_4` is drawn through the origin meeting the lines `L_1a n dL_2` at `A_1a n dB_2,` respectively, such that `P A_1=P B_1dot` Obtain the combined equation of lines `L_3a n dL_4dot`

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CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. Find the equation of the straight line that passes through the point (...

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  2. Find the equation of the line which is parallel to 3x-2y+5=0 and passe...

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  3. Consider two lines L1a n dL2 given by a1x+b1y+c1=0a n da2x+b2y+c2=0 ...

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  4. Find the locus of point P which moves such that its distance from the ...

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  5. Consider two lines L(1) " and " L(2) given by x-y=0 and x+y=0, respect...

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  6. In what ratio does the line joining the points (2, 3) and (4, 1) divid...

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  7. Show that the lines 4x+y-9=0, x-2y+3=0, 5x-y-6=0 make equal intercepts...

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

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  9. A Line through the variable point A(1+k,2k) meets the lines 7x+y-16=0;...

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

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

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

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

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

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

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

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

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

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

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