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If the lines 2a + y 3 = 0, 5x + k y 3 ...

If the lines `2a + y 3 = 0`, `5x + k y 3 = 0`and `3x y 2 = 0`are concurrent, find the value of k.

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given that `L_1, L_2 , L_3 ` are concurrent
`L_1 = 2x+ y -3=0` eqn(1)
`L_2 = 5x + ky - 3=0` eqn(2)
`L_3 = 3x-y-2 = 0` eqn(3)
adding equations `1 & 2:`
`2x + y - 3+ 3x - y-2 = 0`
`5x- 5 = 0`
`x=1`
...
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NCERT-STRAIGHT LINES-SOLVED EXAMPLES
  1. Find the equation of a line perpendicular to the line x-2y+3=0and pas...

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  2. Show that two lines a1x+b1y+c1=0and a2x+b2y+c2=0, where b1,b2!=0are : ...

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  3. If the lines 2a + y 3 = 0, 5x + k y 3 = 0and 3x y 2 = 0are concurr...

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  4. Find the distance of the line 4x y = 0 from the point P(4, 1) measur...

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  5. Assuming that straight lines work as the plane mirror for a point, fi...

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  6. Show that the area of the triangle formed by the lines y=m1x+c1,y=m2x...

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  7. A line is such that its segment between the lines 5x-y + 4 = 0and 3x ...

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  8. Show that the path of a moving point such that its distances from two...

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  9. Write the equation of the line through the points (1, 1)and (3, 5).

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  10. Write the equation of the line for which tantheta=1/2,where thetais th...

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  11. Find the equations of the lines parallel to axes and passing through(...

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  12. Find the equation of the line through ( 2, 3)with slope 4.

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  13. Three points P(h ,k),Q(x1,y1)and R(x2,y2)lie on a line. Show that (h-...

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  14. In Figure, time and distance graph of a linear motion is given. Two p...

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  15. If the angle between two lines is pi/4and slope of one of the lines ...

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  16. Line through the points (-2, 6)and (4, 8)is perpendicular to the line...

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  17. Find the slope of the lines: (a) Passing through the points (3, -2)an...

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  18. Find the equation of line parallel to the y-axis and drawn through th...

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  19. Find the new coordinates of point (3,4) if the origin is shifted to (...

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  20. Find the transformed equation of the straight line 2x - 3y+ 5= 0, whe...

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