If any point on an ellipse is (3sin, 5cos), then what is the eccentricity of the ellipse?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
View all NDA Papers >
  1. 4/3
  2. 4/5
  3. 3/4
  4. 1/2

Answer (Detailed Solution Below)

Option 2 : 4/5
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Calculation:

Given any point on the ellipse is 3sinα, 5cosα. In the standard parametric form of an ellipse,

we identify

Since (b > a), the semi-major axis is (b = 5) and the semi-minor axis is (a = 3). The eccentricity e of an ellipse is

Substitute (a = 3) and (b = 5):

Hence, the correct answer is Option 2.

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

More Parabola, Ellipse and Hyperbola Questions

Hot Links: teen patti royal teen patti master new version teen patti fun teen patti pro