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Prove that the lies 3x+y-14=0,\ x-2y=0\ ...

Prove that the lies `3x+y-14=0,\ x-2y=0\ n a d\ 3x-8y+4=0` are concurrent.

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To prove that the lines \(3x + y - 14 = 0\), \(x - 2y = 0\), and \(3x - 8y + 4 = 0\) are concurrent, we will use the determinant method. The lines are concurrent if the determinant of the coefficients of their equations is zero. ### Step-by-Step Solution: 1. **Write the equations in standard form**: - The equations are already in standard form: 1. \(3x + y - 14 = 0\) 2. \(x - 2y = 0\) (which can be rewritten as \(x - 2y + 0 = 0\)) ...
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RD SHARMA-THE STRAIGHT LINES -Solved Examples And Exercises
  1. Prove that the lines sqrt(3)x+y=0,\ sqrt(3)y+x=0,\ sqrt(3)x+y=1\ a n d...

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  2. Find the equation of the line passing through the intersection of the ...

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  3. Prove that the lies 3x+y-14=0,\ x-2y=0\ n a d\ 3x-8y+4=0 are concurren...

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  4. If the lines a1x+b1y+1=0,\ a2x+b2y+1=0\ a n d\ a3x+b3y+1=0 are concurr...

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  5. Show that the following lines are concurrent: L1=(a-b)x+(b-c)y+(c-a)=0...

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  6. Prove that the following sets of three lines are concurrent: 15 x-18 y...

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  7. Prove that the following sets of three lines are concurrent: x/a+y/b=1...

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  8. For what value of lambda are the three lines 2x-5y+3=0,\ 5x-9y+lambda=...

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  9. Find the conditions that the straight lines y=m1x+c1, y=m2x+c2a n d\ y...

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  10. Show that the straight lines L1=(b+c)x+a y+1=0,\ L2=(c+a)x+b y+1=0\ n ...

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  11. If the three lines a x+a^2y+1=0,\ b x+b^2y+1=0\ a n d\ c x+c^2y+1=0 ar...

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  12. If a ,\ b ,\ c are in A.P. prove that the straight lines a x+2y+1=0,\ ...

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  13. Show that the perpendicular bisectors of the sides of a triangle are c...

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  14. Find the equation of the line which is parallel to 3x-2y+5=0 and passe...

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  15. Find the equation of the straight line that passes through the point (...

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  16. Find equation of the line perpendicular to the line x-7y +5=0 and havi...

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  17. A person standing at the junction (crossing) of two straight paths rep...

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  18. The equations of two sides of a triangle are 3x-2y+6=0\ a n d\ 4x+5y-2...

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

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  20. Find the equation of a line passing through the point (2,3) and par...

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