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For points `P = (x_1, y_1) and Q = (x_2,y_2)` of the coordinate plane, a new distance `d (P, Q)` is defined by `d(P,Q)=|x_1-x_2|+|y_1-y_2|.` Let `O (0, 0)` and `A = (3, 2)`. Prove that the set of points in the first quadrant which are equidistant (wrt new distance) from `O` and `A` consists of the union of a line segment of finite length and an infinite ray. Sketch this set in a labelled diagram.

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ARIHANT MATHS-THE STRAIGHT LINES-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For points P = (x1, y1) and Q = (x2,y2) of the coordinate plane, a new...

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  2. The lines parallel ot the x-axis and passing through the intersection ...

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  3. A straight line through the point A(3, 4) is such that its intercept ...

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  4. If (a,a^(2)) falls inside the angle made by the lines y=(x)/(2), x g...

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  5. The lines L(1) : y - x = 0 and L(2) : 2x + y = 0 intersect the line ...

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  6. Let P = (-1, 0), Q = (0, 0) and R = (3, 3sqrt3) be three points. The e...

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  7. The perpendicular bisector of the line segment joining P (1, 4) and...

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  8. The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicul...

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  9. The line L given by x/5+y/b=1 passes through the point (13, 32). Th...

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  10. A straight line L through the point (3,-2) is inclined at an angle 60^...

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  11. The lines L(1) : y - x = 0 and L(2) : 2x + y = 0 intersect the line ...

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  12. If the line 2x + y = k passes through the point which divides the line...

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  13. A ray of light along x+sqrt(3)y=sqrt(3) gets reflected upon reaching ...

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  14. For a gt b gt c gt 0 if the distance between (1,1) and the point of i...

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  15. Let P S be the median of the triangle with vertices P(2,2), Q(6,-1) ...

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  16. Let a,b, c and d be non-zero numbers. If the point of intersection of...

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  17. For a point P in the plane let d(1)(P)and d(2) be the distance of the ...

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  18. The number of points, having both co-ordinates as integers, that lie i...

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  19. Two sides of a rhombus are along the lines,x-y+1=0 and 7x-y-5=0 . If ...

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