# A rod of length 15 cm moves with its ends always touching the coordinate axes. Find the equation of the locus of a point P on the rod, which is at a distance of 3 cm from the end in contact with the x-axis.

Given: A rod of length 15 cm moves with its ends always touching the coordinate axes. A point P on the rod, which is at a distance of 3 cm from the end in contact with the x-axis

Need to find: Find the equation of the locus of a point P Here AB is the rod making an angle with the x-axis.

Here AP = 3.

PB = AB – AP = 12 – 3 = 9 cm

Here, PQ is the perpendicular drawn from the x-axis and RP is the perpendicular drawn from y-axis.

Let, the coordinates of the point P is (x, y).

Now, in the triangle BPQ,

cos = And in the triangle PAR,

sin = We know, sin2 + cos2 = 1 This is the locus of the point P.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Focal chord of parabola29 mins  Quiz on properties of focal chord of parabola36 mins  Equation of tangent to parabola | Conic Section38 mins  Equation of tangent to parabola | Conic Section | Quiz1 mins  Interactive Quiz on Equation of Parabola41 mins  Lecture on Equation of Parabola59 mins  Applications of +I and -I41 mins  Interactive Quiz on Algae32 mins  Features, similarities and dissimilarities between bryophytes and pteridophytes51 mins  Lecture on Algae46 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 view all courses 