NEET AITS

Mock Tests

Live Class

JEE AITS

Methods of solving first order first degree differential equations

Unlock the full solution & master the concept.

Get a detailed solution and exclusive access to our masterclass to ensure you never miss a concept

By Expert Faculty of Sri Chaitanya

Question

$If the eccentricity of curve for which tangent at point P intersects the y axis at M above x -axis such$
$that origin is equidistant from M and point of tangency, is e, then value of 6 e^{2} is$

Difficult

Solution

We have
$\begin{array}{l} OP = OM \\ \Rightarrow y - x \frac{d y}{d x} = \sqrt{x^{2} + y^{2}} \\ \Rightarrow \frac{d y}{d x} = \frac{y - \sqrt{x^{2} + y^{2}}}{x} \\ \Rightarrow \frac{d y}{d x} = \frac{y}{x} - \sqrt{1 + {(\frac{y}{x})}^{2}} \\ putting \frac{y}{x} = v \Rightarrow \frac{dy}{dx} = v + x \frac{dv}{dx} \\ \Rightarrow v + x \frac{dv}{dx} = v - \sqrt{1 + v^{2}} \\ \Rightarrow \log (v + \sqrt{1 + v^{2}}) = \log \frac{c}{x} \\ \Rightarrow (v + \sqrt{1 + v^{2}}) = \frac{c}{x} \\ \Rightarrow y + \sqrt{x^{2} + y^{2}} = c \\ ⇒curve is parabola \\ ∴ e = 1 \end{array}$

Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

speak to our academic counsellor

access to India's best teachers with a record of producing top rankers year on year.

+91

we will send an otp for verification

799 666 8865

support@infinitylearn.com

6th Floor, NCC Building, Durgamma Cheruvu Road, Vittal Rao Nagar, HITEC City, Hyderabad, Telangana 500081.

free study material

JEE

JEE Mock Tests

JEE study guide

JEE Revision Notes

JEE Important Questions

JEE Sample Papers

JEE Previous Year's Papers

NEET

NEET previous year’s papers

NEET important questions

NEET sample papers

NEET revision notes

NEET study guide

NEET mock tests

CUET

CUET previous year’s papers

CUET important questions

CUET sample papers

CUET revision notes

CUET study guide

CUET mock tests

CBSE

CBSE previous year’s papers

CBSE important questions

CBSE sample papers

CBSE revision notes

CBSE study guide

CBSE mock tests

NCERT solutions

Class 12 NCERT Solutions Class 11 NCERT Solutions Class 10 NCERT Solutions Class 9 NCERT Solutions Class 8 NCERT Solutions Class 7 NCERT Solutions Class 6 NCERT Solutions

NCERT exempler

Class 12 NCERT Exemplar Class 11 NCERT Exemplar Class 10 NCERT Exemplar Class 9 NCERT Exemplar Class 8 NCERT Exemplar Class 7 NCERT Exemplar Class 6 NCERT Exemplar

State Board

Rajasthan State Board West Bengal State Board Gujarat State Board Telengana State Board Andhra Pradesh State Board Uttar Pradesh State Board

Subject

Maths Science Physics Chemistry Economics Accounting Business Studies

2023 | www.infinitylearn.com