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A variable straight line passes through the points of intersection of the lines `x +2y= 1` and `2x-y = 1` and meets the co-ordinates axes in `A` and `B`. Prove that the locus of the midpoint Of `AB` is `10xy = x + 3y`.

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. A straight line segment of length/moves with its ends on two mutually ...

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  2. A line cuts the x-axis at A (7, 0) and the y-axis at B(0, - 5) A varia...

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  3. A variable straight line passes through the points of intersection of ...

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  4. A variable straight line is drawn through the point of intersection of...

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  5. P is the point (-1,2), a variable line through P cuts the x & y axes a...

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  6. A rectangle PQRS has its side PQ parallel to the line y= mx and verti...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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