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If the lines whose equations are y=m1x+c...

If the lines whose equations are `y=m_1x+c_1,y=m_2x+c_2and y=m_3x+c_3` are concurrent, then show that `m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0`.

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MODERN PUBLICATION-STRAIGHT LINES -EXERCISE
  1. For what value of K are the three st. lines : 2x+y-3=0, 5x + ky-3=0 ...

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  2. For what value of K are the three st. lines : 3x+y-2=0,kx+ 2y-3=0 an...

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  3. If the lines whose equations are y=m1x+c1,y=m2x+c2and y=m3x+c3 are con...

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  4. Find the condition that the st. lines : p1x+q1y=1,p2x+q2y=1 and p3x+q3...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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