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If the lines 3x+by-1=0 and ax-5y+2=0 are...

If the lines `3x+by-1=0` and `ax-5y+2=0` are parallel, then find the relation between `a` and `b`.

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To find the relation between \( a \) and \( b \) for the lines \( 3x + by - 1 = 0 \) and \( ax - 5y + 2 = 0 \) to be parallel, we need to equate their slopes. ### Step-by-Step Solution: 1. **Write the equations of the lines in slope-intercept form (y = mx + c)**: - For the first line \( 3x + by - 1 = 0 \): \[ by = -3x + 1 ...
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NAGEEN PRAKASHAN-STRAIGHT LINES-Exercise
  1. If the lines 3x+by-1=0 and ax-5y+2=0 are parallel, then find the relat...

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  2. Find the new co-ordinates of the following points when origin is shift...

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  3. At which point the origin should be shifted such that the new co-ordin...

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  4. If the origin is shifted to the point (1,2) then what will be the tran...

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  5. Find the point at which origin is shifted such that the transformed e...

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  6. Find the point at which is shifted such that the transformed equations...

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  7. Find the point at which origin is shifted such that the transformed eq...

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  8. Show that the area of triangle whose vertices are (1,0), (2,4) and (3,...

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  9. Find the slope of the lines whose iclination is given : (i) 45^(@) (...

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  10. Find the inclination of the lines whose slopes are as follows : (i) ...

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  11. Find the slopes of the lines passing through the following points : ...

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  12. If the slope of a line passing through the points (1,4) and (x,2) is 2...

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  13. If the angle of inclination of line joining the points (x,3) and (-2,5...

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  14. If the slop of line joining the points (6,-3) and (x,7) is 2, find the...

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  15. Show that the line joining the points (4,-1) and (-3,3) is parallel to...

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  16. If the line joining the points (5,y) and (4,9) is parallel to the line...

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  17. Show that the line joining the points (4,-3) and (0,7) is perpendicula...

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  18. If the line joining the points (6,-2) and (8,4) is perpendicular to th...

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  19. Without using Pythagoras theorem, show that A(4,4),\ B(3,5)a n d\ C(-1...

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  20. Using slopes, show that the points A(0,5), B(3,2) and C(-1,6) are coll...

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  21. Using the slope of line, show that the points (-1,-2), (0,4), (3,3) an...

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