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If a and b are real numbers between o and 1 such that the points (a,0), (1,b) and (0,0) form an equilateral triangle then a=_______ and b=_________.

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. The distance of (1,2) from the line 3x-4y+15=0 measured parallel to th...

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  2. The set of lines ax + by+ c= 0, where 3a+ 2b+ 4c =0, is concurrent at ...

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  3. If a and b are real numbers between o and 1 such that the points (a,0)...

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  4. If a , ba n dc are in A P , then the straight line a x+b y+c=0 will al...

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  5. Let the algebraic sum of the perpendicular distances from the points (...

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  6. If the point (2a-3, a^2-1) is on the same side of the line x+y-4=0 as ...

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  7. The points (-a,-b), (0,0). (a,b) and (a^(2),a^(3)) are

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  8. The points (0,(8)/(3)), (1,3) and (82,30) are vertices of

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  9. 15. The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 IS: (c...

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  10. The straight lines x+y=0, 3x+y-4=0 and x+3y-4=0 form a triangle which ...

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  11. Three lines px+qy+r=0, qx+ry+p=0 and rx+py+q=0 are concurrent , if

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  12. Given four lines whose equations are x +2y -3=0, 2x+3y-4=0, 3x + 4y -7...

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  13. If P(1,0), Q(-1,0) and R (2,0) are three given points, then the locus ...

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  14. If the sum of the distances of a point from two perpendicular lines in...

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  15. The image of the point (-1,3) by the line x - y = 0 , is

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  16. The point (4, 1) undergoes the following three transformations success...

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  17. All points lying inside the triangle formed by the points (1,3) ,(5,0)...

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  18. The two line segment joining (-2,7), (-5,-3) and (-8,-13),(1,17) cut e...

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  19. If line y - x + 2 = 0 is shifted parallel to itself towards the x-axis...

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  20. If the point (a^2,a+1) lies in the angle between the lines 3x-y+1=0 an...

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