Q. 104.3( 3 Votes )

Find the equation of a straight line on which the perpendicular from the origin makes an angle of 30° with x–axis and which forms a triangle of the area with the axes.

Answer :

Assuming: AB be the given line, and OL = p be the perpendicular drawn from the origin on the line.


Given: α = 60°


Explanation:


So, the equation of the line AB is


x cos θ + y sin θ = p


x cos 30 + y sin 30 = p



√3x + y = 2p …… (1)


Now, in triangles OLA and OLB


Cos 30° = , cos6° =


,


OA = and OB = 2p


It is given that the area of triangle OAB is 503




p2 = 75


p = √75


Substituting the value of p in (1)


√3 x + y = √75


Hence, the equation of the line AB is √3 x + y = √75


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of lineVarious Forms of Equations of lineVarious Forms of Equations of line45 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Slope, inclination and angle between two linesSlope, inclination and angle between two linesSlope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of lineInteractive Quiz on Equations of lineInteractive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quizStraight line | Analyse your learning through quizStraight line | Analyse your learning through quiz56 mins
General Equation of a lineGeneral Equation of a lineGeneral Equation of a line43 mins
Motion in a Straight Line - 06Motion in a Straight Line - 06Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 05Motion in a Straight Line - 05Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 03Motion in a Straight Line - 03Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 11Motion in a Straight Line - 11Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses