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Show that the line x-y-6=0,4x-3y-20=0 an...

Show that the line `x-y-6=0,4x-3y-20=0` and `6x+5y+8=0` are concurrent. Also, find their common point of intersection.

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To show that the lines \( x - y - 6 = 0 \), \( 4x - 3y - 20 = 0 \), and \( 6x + 5y + 8 = 0 \) are concurrent, we need to check the condition for concurrency. The lines are concurrent if the determinant formed by their coefficients is zero. ### Step 1: Write the equations in standard form The given equations are: 1. \( x - y - 6 = 0 \) 2. \( 4x - 3y - 20 = 0 \) 3. \( 6x + 5y + 8 = 0 \) ...
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RD SHARMA ENGLISH-THE STRAIGHT LINES -All Questions
  1. Two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y=0. If t...

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  2. Find the equation of the straight line passing through the point of ...

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  3. Show that the line x-y-6=0,4x-3y-20=0 and 6x+5y+8=0 are concurrent. Al...

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  4. Three sides A B ,A Ca n dC A of triangle A B C are5x-3y+2=0,x-3y-2=0a ...

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  5. Find the coordinates of the incentre and centroid of the triangle whos...

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  6. Show that the straight lines given by x(a+2b)+y(a+3b)=a for different ...

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  7. If a ,b ,c are variables such that 3a+2b+4c=0 , then show that the fam...

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  8. If the algebraic sum of the perpendiculars from the points (2,0),(0,2)...

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  9. A ray of light is sent along the line x-2y-3=0 upon reaching the line ...

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  10. lines L1:ax+by+c=0 and L2:lx+my+n=0 intersect at the point P and make ...

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  11. Find the equation of the straight line passing through the point of ...

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  12. Find the equation of the straight line which cuts off intercept on ...

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  13. Find the equation of the straight line passing through the point of ...

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  14. Find the equations of the lines through the point of intersection of t...

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  15. If the diagonals of the quadrilateral formed by lines l1x+m1y+n1=0, l...

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  16. Write the area of the figure formed by the lines a|x|+b|y|+c=0.

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  17. If theta is the acute angle between the lines with slopes m1 and m2 th...

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  18. A straight line L is perpendicular to the line 5x-y=1. The area of the...

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  19. Find the image of the point (-8,12) with respect to line mirror 4x+7y+...

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  20. Show that the equation of a line passing through (acos^3theta,asin^3th...

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