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If a,b,c are arithmetic progression then show that the equation `ax+by+c=0` represents a family of concurrent lines and find the point of concurrency.

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AAKASH SERIES-STRAIGHT LINES-SOLVED EXAMPLES
  1. The three straight lines px+qy+r=0, qx+ry+p=0 ane rx+py+q=0 are concur...

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  2. Find the point of concurrence of the set of lines (2+5k)x-3(1+2k)y+(...

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  3. If a,b,c are arithmetic progression then show that the equation ax+by...

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  4. Find the equation of the straight line passing through the point of in...

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  5. Find the line passing through the point of intersection of the lines x...

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  6. The points (1, 3) and (5, 1) are two opposite vertices of a rectangle....

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  7. Find the orthocentre of the triangle formed by the vertices (-2,-1),(6...

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  8. Find the orthocentre of the triangle formed by x+y+10=0,x-y-2=0, 2x+y-...

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  9. Find the orthocentre of the triangle formed by the lines x+2y=0,4x+3y=...

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  10. Two vertices of a triangle are (5,-1) and (-2,3). If the orthocentre ...

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  11. Find the circumcentre of the triangle formed by the points (2,1),(1,-2...

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  12. Find the circumcentre of the triangle whose vertices are A(1,0),B(-1,2...

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  13. Find the circumcentre of the triangle formed by the lines x+y=0, 2x+y+...

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  14. Find the circumcentre of the triangle whose sides are 3x-y-5=0, x+2y-4...

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  15. Find the incenter of the triangle formed by the straight lines y=sqrt(...

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  16. Find the incentre of the triangle formed by x+y-7=0,x-y+1=0,x-3y+5=0.

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  17. A triangle is formed by the lines ax+by+c=0, lx+my+n=0 and px+qy+r=0. ...

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  18. The Cartesian equation of the sides BC,CA, AB of a triangle are respec...

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  19. Find the acute angle between the lines y+2=0 and sqrt(3)x+y-1=0.

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  20. Find the value of k if the lines 2x+ky-10=0 and 5x+2y-7=0 are parallel...

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