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Show that the straight lines given by `(2+k)x+(1+k)y=5+7k` for different values of `k` pass through a fixed point. Also, find that point.

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To show that the straight lines given by the equation \((2+k)x + (1+k)y = 5 + 7k\) pass through a fixed point for different values of \(k\), we can follow these steps: ### Step 1: Rearranging the Equation We start with the equation: \[ (2+k)x + (1+k)y = 5 + 7k \] We can rearrange this to group the terms involving \(k\): ...
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RD SHARMA-THE STRAIGHT LINES -Solved Examples And Exercises
  1. Show that the straight lines given by (2+k)x+(1+k)y=5+7k for different...

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  2. Find the equation of the internal bisector of angle B A C of the trian...

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  3. In what ratio, the line joining (-1,1)a n d(5,7) is divided by the lin...

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  4. The mid points of the sides of a triangle are (2,1), (-5,7) and (-5,-5...

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  5. Find the equation of the altitudes of the triangle whose vertices are ...

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  6. One side of a square makes an angle alpha with x axis and one vertex o...

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  7. Show that the perpendicular drawn from the point (4,1) on the line seg...

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  8. Prove that the perpendicular drawn from the point (4,1) on the join of...

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  9. A line passing through the point A(2,0) makes 30^0 angle with the posi...

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  10. In what ratio is the line joining the points (2,3)a n d(4,1) divides t...

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  11. Find the equations to the altitudes of the triangle whose angular po...

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  12. Find the equations of the diagonals of the square formed by the lines ...

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  13. Find the equation of a line which cuts off intercepts a and b respecti...

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  14. Find the equation of the bisector of angle A ofthe triangle whoe verti...

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  15. Find the equations the straight lines which go through the origin and ...

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  16. A line is such that its segment between the lines 5x" "" "y" "+" "4...

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  17. Find the equations to the diagonals of the rectangle the equations of ...

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  18. A rectangle has two opposite vertices at the points (1,2)a n d(5,5)dot...

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  19. Find the coordinates of the vertices of a square inscribed in the tria...

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  20. If the intercept of a line between the coordinate axes is divided by ...

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