InterviewSolution
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InterviewSolution
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Angle made with the x-axis by a straight line drawn through (1, 2) sothat it intersects `x+y=4`at a distance `(sqrt(6))/3`from (1, 2) is`105^0`(b) `75^0`(c) `60^0`(d) `15^0`A. `pi//6 and pi//3`B. `pi//8 and 3pi//8`C. `pi//12 and 5pi//12`D. none of these |
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Answer» Correct Answer - C Suppose a line passing through (1,2) makes an angle `theta` with x-axis . Then, its equation is `(x-1)/(cos theta)=(y-2)/(sin theta)` The coordinates of a point on this line at a distance `(sqrt(16))/(3)=sqrt((2)/(3))` from (1,2) are given by `(x-1)/(costheta)=(y-2)/(sin theta)=sqrt((2)/(3))` or, `(1+sqrt((2)/(3)) costheta, 2+sqrt((2)/(3)) sin theta)` This point lies on `x+y=4` `therefore 1+sqrt((2)/(3)) costheta + 2+ sqrt((2)/(3)) sin theta=4` `implies cos theta + sin theta=sqrt((3)/(2))` `implies sin (theta+(pi)/(4))=(sqrt(3))/(2)implies theta=(pi)/(12) and (5pi)/(12)` |
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