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If the four straight lines ax+by+p=0, ax...

If the four straight lines `ax+by+p=0, ax+by+q=0, cx+dy+r=0` and `cx+dy+s=0` form a prallelogram. Show that the area of the parallelogram so formed is
`|((p-q)(r-s))/(bc-ad)|`

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Verified by Experts

The correct Answer is:
`=(|bc-ad|)/(sqrt((a^(2)+b^(2))(c^(2)+d^(2))))`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-STRAIGHT LINE -TEXTUAL EXERCISES (EXERCISE-3(e))
  1. If the four straight lines ax+by+p=0, ax+by+q=0, cx+dy+r=0 and cx+dy+s...

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  2. Find the incentre of the Delta^(l e) with the vertices (1,sqrt3),(0,0)...

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  3. Find the orthocentre of the triangle whose sides are given by x+y+10=0...

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  4. The orthocentre of the triangle whose sides are given by 4x-7y+10=0,x+...

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

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  6. The incentre of the triangle formed by the lines x+y=1,x=1,y=1 is

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

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  8. Find the value of k if the angle between the straight kx+y+9=0, 3x-y+4...

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  9. Find the equation of the straight line passing through (0,0) and also ...

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  10. Find the equation of the straight line parallel to 3x+4y=7 and passing...

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  11. The equation of the straight line perpendicular to the straight line 3...

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  12. Find the equation of the straight line making non zero equal intercept...

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  13. Find the point of intersection of the lines 4x+8y-1=0, 2x-8y+1=0

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  14. Find the value of a if the distances of the points (2,3) and (-4,a) fr...

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

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  16. If theta is the angle between the lines x/a+y/b=1 and x/b+y/a=1 find t...

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  17. Find the equation of the straight lines passing through the point (-10...

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  18. Find the equation of the straight lines passing through the point (1,2...

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  19. The base of an equilateral triangle x + y = 2 = 0 and opposite vertex...

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  20. Find the orthocentre of the triagle whose vertices are (-2,-1)(6,-1),(...

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  21. Find the orthocentre of the triangle whose vertices are (5,-2),(-1,2),...

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