Find the equation of the circle that passes through the points (-1, 0), (1, 0) and (0, -1).

  1. x2 + y2 = 1 
  2. x2 + y2 = 0 
  3. x2 + y2 = -1 
  4. x2 + y2 = 2 

Answer (Detailed Solution Below)

Option 1 : x2 + y2 = 1 
Free
Agniveer Navy SSR Full Test - 01
4.1 K Users
100 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

Concept:

The general form of the equation of a circle is:

x2 + y2 + 2gx + 2fy + c = 0

  • The center of the circle is (-g, -f).
  • The radius of the circle is \(\sqrt{g^{2}+f^{2}-c}\)

Calculation:

Let the required circle be x2 + y2 + 2gx + 2fy + c = 0      ----(1)

It passes through (-1, 0), (1, 0) and (0, -1).

Therefore, on substituting the coordinates of three points successively in equation (1), we get

1 - 2g + c = 0      ----(2)

1 + 2g + c = 0      ----(3)

1 - 2f + c = 0      ----(4)

Subtracting equation (2) from the (3), we get

4g = 0

⇒ g = 0

On putting the value of g in equation (3), we get

c = -1

Now, putting the value of c in equation (4), we get

1 - 2f - 1 = 0

⇒ f = 0

On substituting the value of g, f, and c in equation (1), we get

x2 + y2 - 1 = 0

⇒ x2 + y2 = 1 

Hence, the required equation is x2 + y2 = 1.

Latest Indian Navy Agniveer SSR Updates

Last updated on May 31, 2025

-> The Indian Navy SSR Agniveeer Merit List will be released soon on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

More Circles Questions

Get Free Access Now
Hot Links: teen patti vungo teen patti rummy 51 bonus teen patti royal - 3 patti teen patti gold old version