Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

A rod of length 12 cm moves with it ends always touching the c

Question

A rod of length $12$ cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point $P$ on the rod which is $3$ cm from the end in contact with the $x$ -axis

Views: 985 students

Found 4 tutors discussing this question

Noah Discussed

A rod of length

12

cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point

P

on the rod which is

3

cm from the end in contact with the

x

-axis

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Let

A B

be the rod making an angle

θ

with positive direction of

x

-axis and

P (x, y)

be the point on it such that

A P = 3 c m

Now,

PB = A B - A P = (12 - 3) c m = 9 c m

(A B = 12 c m)

Draw

PQ ⊥ O Y

and

PR ⊥ OX

△ PBQ

cos θ = \frac{PQ}{PB} = \frac{x}{9}

△ PR A

sin θ = \frac{PR}{P A} = \frac{y}{3}

Since

sin^{2} θ + cos^{2} θ = 1

\Rightarrow (\frac{y}{3})^{2} + (\frac{x}{9})^{2} = 1

\Rightarrow \frac{x ^{2}}{81} + \frac{y ^{2}}{9} = 1

Thus the equation of the locus of point

P

on the rod is

\frac{x ^{2}}{81} + \frac{y ^{2}}{9} = 1

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	A rod of length $12$ cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point $P$ on the rod which is $3$ cm from the end in contact with the $x$ -axis
Answer Type	Text solution:1
Upvotes	150

A rod of length 12 cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point P on the rod which is 3 cm from the end in contact with the x-axis

Text solutionVerified

Practice questions from similar books

A rod of length $12$ cm moves with it ends always touching the coordinate axes. Dertermine the equation of the locus of a point $P$ on the rod which is $3$ cm from the end in contact with the $x$ -axis