Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Orthogonal trajectory for x^2 + y^2 =a^2(a is parameter) will be

  • Option 1)

    y^2 = cx

  • Option 2)

    y= cx^2

  • Option 3)

    y= cx

  • Option 4)

    y + x = c

 

Answers (1)

best_answer

As we have learnt,

 

Orthogonal Trajectory -

Any curve which cuts every member of a given family of curves at right angles

- wherein

 

 First of all we need defferential equation for given family of curves. So on differentiating we get,

2x +2y\frac{\mathrm{d} y}{\mathrm{d} x} = 0 \Rightarrow \frac{\mathrm{d} y} {\mathrm{d} x} = -\frac{x}{y}

Now, If replace \frac{\mathrm{d} y}{\mathrm{d} x} by -\frac{\mathrm{d} x}{\mathrm{d} y}, the obtained equation will be differential equation for required orthogonal trajectory.

So, we get

-\frac{\mathrm{d} x}{\mathrm{d} y} = -\frac{x}{y}\Rightarrow \frac{dx}{x} = \frac{dy}{y}

\Rightarrow On integrating we get

\ln x - \ln y = c\Rightarrow \frac{x}{y} = e^c \Rightarrow \frac{x}{y} = c \Rightarrow y = cx

 


Option 1)

y^2 = cx

Option 2)

y= cx^2

Option 3)

y= cx

Option 4)

y + x = c

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question