Q. 103.5( 2 Votes )

A rod of length l slides between the two perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

Answer :

Key points to solve the problem:


Idea of distance formula- Distance between two points A(x1,y1) and B(x2,y2) is given by- AB =


Idea of section formula- Let two points A(x1,y1) and B(x2,y2) forms a line segment. If a point C(x,y) divides line segment AB in the ratio of m:n internally, then coordinates of C is given as:


C =


How to approach: To find the locus of a point we first assume the coordinate of the point to be (h, k) and write a mathematical equation as per the conditions mentioned in the question and finally replace (h, k) with (x, y) to get the locus of the point.


Let the coordinates of a point whose locus is to be determined to be (h, k). Name the moving point to be C


Assume the two perpendicular lines on which rod slides are x and y-axis respectively.



Here line segment AB represents the rod of length l also ΔADB formed is a right triangle. Coordinates of A and B are assumed to be (0,b) and (a,0) respectively.


a2 + b2 = l2…eqn 1


As, (h,k) divides AB in ratio of 1:2


from section formula we have coordinate of point C as-


C = =


As, a and b are assumed parameters so we have to remove it.


h = 2a/3 a = 3h/2


And k = b/3 b = 3k


From eqn 1:


a2 + b2 = l2




Replace (h,k) with (x,y)


Thus, the locus of a point on the rod is: ….ans


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Moment of Inertia | Some special casesMoment of Inertia | Some special casesMoment of Inertia | Some special cases40 mins
GTSE 2020 (August) Chemistry Important QuestionsGTSE 2020 (August) Chemistry Important QuestionsGTSE 2020 (August) Chemistry Important Questions30 mins
Important Questions for GTSE Aug 2020 (Maths)Important Questions for GTSE Aug 2020 (Maths)Important Questions for GTSE Aug 2020 (Maths)30 mins
NCERT Exemplar Special | Animal Kingdom Part 1NCERT Exemplar Special | Animal Kingdom Part 1NCERT Exemplar Special | Animal Kingdom Part 130 mins
NCERT Exemplar Special | Animal Kingdom Part 2NCERT Exemplar Special | Animal Kingdom Part 2NCERT Exemplar Special | Animal Kingdom Part 231 mins
Important Questions for GTSE Aug 2020 (Chemistry)Important Questions for GTSE Aug 2020 (Chemistry)Important Questions for GTSE Aug 2020 (Chemistry)39 mins
GTSE Sample Paper and Imp. Question Discussion | Chemistry | Mritunjay SirGTSE Sample Paper and Imp. Question Discussion | Chemistry | Mritunjay SirGTSE Sample Paper and Imp. Question Discussion | Chemistry | Mritunjay Sir42 mins
NCERT Exemplar Special | Biomolecules Part 1NCERT Exemplar Special | Biomolecules Part 1NCERT Exemplar Special | Biomolecules Part 126 mins
Interactive Quiz on Equivalent ConceptInteractive Quiz on Equivalent ConceptInteractive Quiz on Equivalent Concept61 mins
Interactive Quiz on Mole concept - 2Interactive Quiz on Mole concept - 2Interactive Quiz on Mole concept - 264 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