What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are and ?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
View all NDA Papers >
  1. x2+y2=1
  2. x2+y2=25
  3. x2+y2=100
  4. x2+y22x2y23=0

Answer (Detailed Solution Below)

Option 2 : x2+y2=25
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
6 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Calculation:

Given two diameters of the circle are along the lines x + y = 0 and x - y = 0. The center of the circle is at their intersection.

We have, 

\(x - y = 0 \;\Longrightarrow\; x = y.\)

Substitute into x + y = 0:

\(x + x = 0 \;\Longrightarrow\; 2x = 0 \;\Longrightarrow\; x = 0,\; y = 0.\)

Thus, the center is (0, 0).

Also radius,

\(r = \frac{10}{2} = 5.\)

the equation of the circle with center (0,0) and radius 5 is

\(x^{2} + y^{2} = 5^{2} = 25.\)

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 Circles Questions

Get Free Access Now
Hot Links: teen patti stars teen patti sequence teen patti vip