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Let P-=(-1,0),Q-=(0,0), "and " R-=(3,3sq...

Let `P-=(-1,0),Q-=(0,0), "and " R-=(3,3sqrt(3)) " be three points".`
Then the equation of the bisector of `angle PQR` is

A

`(sqrt(3))/(2)x+y=0`

B

`x+sqrt(3)y=0`

C

`sqrt(3)x+y=0`

D

`x+(sqrt(3))/(2)y=0`

Text Solution

Verified by Experts

The correct Answer is:
C
The bisector of angle PQR divides PR in the ratio PQ:QR i.e. 1:6 . So, the coordinate of the point of divison are
`((1xx3+6xx-1)/(6),(1xx3sqrt(3)+6xx0)/(1+6))=((-3)/(7),(3sqrt(3))/(7))`
Clearly , required bisector passes through Q(0,0) and `(-3//7,3sqrt(3)//7)`. So, its equation is
`y-0 =((3sqrt(3))/(7)-0)/(-(3)/(7)-0)(x-0) implies y=-sqrt(3)x implies sqrt(3)x+y=0`
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OBJECTIVE RD SHARMA ENGLISH-STRAIGHT LINES-Chapter Test
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  2. The equation to a pair of opposite sides of a parallelogram are x^2-5x...

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  3. The distance between the parallel lnes y=2x+4 and 6x-3y-5 is (A) 1 (B)...

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  4. P is a point on either of the two lines y - sqrt(3)|x| = 2 at a dista...

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  5. If one diagonal of a square is along the line x=2y and one of its vert...

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  6. The line which is parallel to x-axis and crosses the curve y=sqrt(x) a...

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  7. P(3,1),Q(6,5) and R(x,y) are three points such that PRQ is a right ang...

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  8. Find the equation of the straight line which passes through the point ...

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  9. What is the equation of the straight line which is perpendicular to y=...

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  10. Find the perpendicular distance between the lines 3x+4y+9=0 and to 6x...

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  11. The equation of the line passing through the point (1,2) and perpendic...

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  12. The straight lines x+y=0, 3x+y-4=0 and x+3y-4=0 form a triangle which ...

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  13. Triangle formed by x^(2)-3y^(2)=0 and x=4 is

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  14. The co-ordinates of the orthocentre of the triangle bounded by the lin...

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  15. the lines (p+2q)x+(p-3q)y=p-q for different values of p&q passes troug...

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  16. Write the distance between the lines 4x+3y-11=0\ a n d\ 8x+6y-15=0.

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  17. If the diagonals of a parallelogram ABCD are along the lines x+5y=7 a...

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  18. The straight lines x+y-4=0, 3x+y-4=0 and x+3y-4=0 form a triangle, whi...

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  19. Write the coordinates of the orthocentre of the triangle formed by ...

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  20. A point equidistant from the line 4x + 3y + 10 = 0, 5x-12y + 26 = 0 an...

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  21. The number of values of a for which the lines 2x+y-1=0 , a x+3y-3=0, a...

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