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Prove that the diagonals of the parallel...

Prove that the diagonals of the parallelogram formed by the four lines : `x/a +y/b=1,x/b+y/a= 1, x/a + y/b = -1 and x/b + y/a = -1` are at right angles .

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MODERN PUBLICATION-STRAIGHT LINES -EXERCISE
  1. Find the condition that the st. lines : p1x+q1y=1,p2x+q2y=1 and p3x+q3...

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  2. Find the foot of the perpendicular from the point (-1, 2) on the st. l...

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  3. Prove that the diagonals of the parallelogram formed by the four lines...

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  4. Prove that the following lines are concurrent. Also, find the point of...

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  5. Prove that the following lines are concurrent. Also, find the point of...

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  6. The sides of a triangle are given by : x-2y+9=0, 3x + y-22 =0 and x + ...

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  7. Obtain the co-ordinates of the feet of perpendiculars drawn from the o...

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  8. Vertices of a triangle are (-1, 3), (2, -1), (0, 0). Find its orthocen...

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  9. A triangle is determined by the lines : y+x-6=0, 3y-x + 2 = 0, 3y = 5x...

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  10. Two vertices of a triangle are (3,- 1) and (- 2, 3) and its orthocentr...

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  11. Find the co-ordinates of the incentre of the triangle formed by the li...

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  12. Find the co-ordinates of the circumcentre of the triangle whose vertic...

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  13. Find the co-ordinates of the circumcentre of the triangle whose vertic...

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  14. Find the area of the triangle formed by the lines y-x=0, x+y=0 and x-k...

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  15. Prove analytically that the : medians of a triangle are concurrent.

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  16. Prove analytically that the altitudes of a triangle are concurrent.

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  17. The co-ordinates of points A, B and C are (1, 2),(-2, 1) and (0, 6) re...

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  18. Prove that the diagonals of a square are equal.

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  19. Which of the following statements are True or False : The diagonals of...

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  20. Say True or False: The diagonals of a square are perpendiculare to one...

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