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Locus of the middle point of the interce...

Locus of the middle point of the intercept on the line ` y = x + c ` made by the lines `2x + 3y = 5` and `2x + 3y = 8`, `c` being a parameter is

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. A rectangle PQRS has its side PQ parallel to the line y= mx and verti...

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  2. A point P\' move along the y-axis. Another point Q moves so that the f...

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  3. Locus of the middle point of the intercept on the line y = x + c ma...

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  4. Two points Pa n dQ are given. R is a variable point on one side of ...

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  5. Let L1=0a n dL2=0 be two fixed lines. A variable line is drawn through...

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  6. A variable straight line passes through a fixed point (h,k). Find the ...

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  7. A straight lien is drawn from a fixed point O metting a fixed straight...

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  8. The point P(1,1,1) is transiated parallel to 2x=yin the first quadrant...

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  9. Two particles start from the point (2, -1), one moving 2 units along t...

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  10. The line 2x-y = 5 turns about the point on it, whose ordinate and absc...

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  11. The line x+ 2y=4 is-translated parallel to itself by 3 units in the se...

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  12. A ray of light coming fromthe point (1, 2) is reflected at a point A o...

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  13. A man starts from the point P(-3, 4) and will reach the point Q(0, 1) ...

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  14. A beam of light is sent along the line x-y=1 , which after refracting ...

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  15. Show that the points (-2,3), (8, 3) and (6, 7) are the vertices of a r...

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  16. The points (1, - 2), (-3,0) and (5,6) are the vertices of aright angle...

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  17. The distance of (1,2) from the line 3x-4y+15=0 measured parallel to th...

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

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

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  20. 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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