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if the straight line through the point P(3,4) makes an angle π/6 with x-axis in anticlockwise sense and meets the line 12x+5y+10=0 at Q,then the length of PQ= 132/12√3+5 132/12√3-5 13/12√3-5 none of these

if the straight line through the point P(3,4) makes an angle π/6 with x-axis in anticlockwise sense and meets the line 12x+5y+10=0 at Q,then the length of PQ=
  • 132/12√3+5
  • 132/12√3-5
  • 13/12√3-5
  • none of these

Grade:11

2 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
9 years ago
Hi Student

Using point slope form , equation of above line is
y-4 =1/\sqrt{3} ( x-3)

from Second equation
y= (-10-12x)/5

Solve the 2 equation and get the point Q

Using distance formula find PQ.
Ravi
askIITians Faculty 69 Points
9 years ago
Form the eqn of a line passing through the point P(3,4) and has a slope equal to tan(theta) where theta is the angle the line makes with the positive direction of X axis in clockwise dirrection. Hence, theta acc. to the question would be Theta=5pi/6.

The equation of line whose eqn has been derived meets the line12x+5y+10=0 at Q. Solve the 2 eqns and obtain the coordinates of Q. Then using distance formula, find the length of Q.

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