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Let L be the line belonging to the famil...

Let L be the line belonging to the family of straight lines (a+2b) x+(a-3b)y+a-8b =0, a, b `in `R, which is the farthest from the point (2, 2).
If L is concurrent with the lines x-2y+1=0 and `3x-4y+ lambda=0`, then the value of `lambda` is

A

2

B

1

C

-4

D

5

Text Solution

Verified by Experts

The correct Answer is:
D
Lines x+4y+7 =0 and x-2y+1 =0 intersect at (-3, -1) which must satisfy the line `3x-4y+lambda=0. "Then " -9+4+lambda=0 " or " lambda = 5.`
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CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (LINKED COMPREHENSION TYPE)
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  2. Let L be the line belonging to the family of straight lines (a+2b) x+(...

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  3. Let L be the line belonging to the family of straight lines (a+2b) x+(...

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  5. The equation of an altitude of an equilateral triangle is sqrt3x + y =...

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  6. The equation of an altitude of an equilateral triangle is sqrt(3)x+y =...

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  7. A variable line L is drawn through O (0,0) to meet the lines L 1 ​ ...

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  8. A variable line L is drawn through O(0,0) to meet the line L(1) " and ...

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  9. A variable line L is drawn through O(0,0) to meet the line L(1) " and ...

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  10. The line 6x+8y=48 intersects the coordinates axes at A and B, respeciv...

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  11. if a line has direction ratio 2,-1,-2,determine its direction cosine

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  12. The line 6x+8y=48 intersects the coordinates axes at A and B, respeciv...

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  13. A(1,3) and C(-2,/5, -2/5) are the vertices of a triangle ABC and the e...

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  14. A(1,3)and c(-2/5,-2/5)are the vertices of a DeltaABCandthe equation of...

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  15. A(1,3) and C(-2,/5, -2/5) are the vertices of a triangle ABC and the e...

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  16. Let ABCD be a parallelogram the equation of whose diagonals are AC : x...

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  17. Let ABCD be a parallelogram the equation of whose diagonals are AC : x...

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  18. Let ABCD be a parallelogram the equation of whose diagonals are AC : x...

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  19. Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q...

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  20. Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q...

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