JEE Main Class 11 Syllabus 2025 PDF for Paper 1 and 2

Diametric Form of a Circle - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

Diametric Form of a Circle is considered one the most difficult concept.
8 Questions around this concept.

Solve by difficulty

The intercept on the line $\mathrm{y=x}$ by the circle $\mathrm{x^{2}+y^{2}-2 x=0}$ is $\mathrm{A B}$ . The equation of the circle with $\mathrm{A B}$ as a diameter is:

A

$\mathrm{x^{2}+y^{2}+x+y=0}$

B

$\mathrm{x^{2}+y^{2}-x-y=0}$

C

$\mathrm{x^{2}+y^{2}+x-y=0}$

D

none of these

One of the diameters of the circle circumscribing the rectangle $\mathrm{A B C D}$ is $\mathrm{4 y=x+7}$ . if $\mathrm{A}$ and $\mathrm{b}$ are $(-3,4),(5,4)$ , the area of the rectangle is

A

16 sq. units

B

24 sq. units

C

32 sq. units

D

48 sq. units

Concepts Covered - 1

Diametric Form of a Circle

Diametric Form of a Circle:

The equation of circle, when endpoints A (x₁, y₁) and B(x₂, y₂) of a diameter are given, is

$\mathrm{\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0}$

Proof:

P(x,y) is any point on the circle

$\\ \text { Slope of } \mathrm{AP}=\frac{\mathrm{y}-\mathrm{y}_{1}}{\mathrm{x}-\mathrm{x}_{1}} \\ \text { Slope of } \mathrm{BP}=\frac{\mathrm{y}-\mathrm{y}_{2}}{\mathrm{x}-\mathrm{x}_{2}} \\\because \angle \mathrm{APB}=90^{\circ} \\\therefore \text{Slope of }\mathrm{AP} \times \mathrm{Slope\; of \;}\mathrm{BP}=-1\\ \mathrm{\Rightarrow\left(\frac{y-y_{1}}{x-x_{1}}\right) \times\left(\frac{y-y_{2}}{x-x_{2}}\right)=-1} \\ \mathrm{\Rightarrow\left(x-x_{1}\right)\left(x-x_{2}\right)+\left(y-y_{1}\right)\left(y-y_{2}\right)=0}$

Study it with Videos

Diametric Form of a Circle

Study other Related Concepts

Diametric Form of a Circle Current Topic

Coordinate Axes

Distance Between Two Points Formula

Section Formula & Conic Sections

Centroid, Incentre and Circumcentre and Orthocentre of a Triangle

Excenters of Triangle

Circumcentre and Orthocentre

Area of Triangle in Coordinate Geometry

Transformations of Axes

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Books

Reference Books

Diametric Form of a Circle

Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry

Page No. : 4.9

Line : 5

Clear your Basics with NCERT

NCERT Solutions for Class 11 Maths (2024-25)

July 04, 2019

NCERT Solutions for Class 12 Maths - Get Free PDFs 2024-25

June 10, 2019

E-books & Sample Papers

JEE Main 2025 Paper 2 (B.Arch) Syllabus

776+ Downloads

JEE Main 2025 Math Syllabus

8533+ Downloads

Get Answer to all your questions

JEE Main Articles

JEE Mains 2025 - Registration (Open), Exam Dates Out, Syllabus, Pattern, Previous Year Papers

Nov 18, 2024

Why is NTA Rejecting JEE Main Application Form 2025?

Nov 18, 2024

JEE Main Form Correction 2025 - Date, Procedure, Guidelines, Fee

Nov 18, 2024

How to Check JEE Mains Exam Centre 2025

Nov 18, 2024

JEE Main Result 2025 - Date, BE, BTech, BArch, BPlan Results Link

Nov 18, 2024

JEE Main 2025 Latest News and Updates Today

Nov 18, 2024

IIT Kanpur JEE Main 2025 Preparation - 45 Days Days Crash Course SATHEE

Nov 18, 2024

Lowest JEE Main Registration this Year? - Students Face Issues in Application, Check Trends

Nov 18, 2024

B.Tech/B.Arch Admissions OPEN

UPES B.Tech Admissions 2025

Ranked #42 among Engineering colleges in India by NIRF | Highest CTC 50 LPA , 100% Placements

Dayananda Sagar University B.Tech Admissions 2025

60+ Years of Education Legacy | UGC & AICTE Approved | Prestigious Scholarship Worth 6 Crores | H-CTC 35 LPA

Parul University B.Tech Admissions 2025

India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package

Lovely Professional University B.Tech Admissions 2025

India's Largest University | NAAC A++ Accredited | 100% Placement Record | Highest Package Offered : 3 Cr PA

Atlas SkillTech University | B.Tech Admissions

Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application

Pearson | PTE

Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 30th NOV'24! Trusted by 3,500+ universities globally

View All Application Forms

News and Notifications

JEE Mains 2025: Application correction facility from November 26 to 27; NTA answers FAQs

November 18, 2024 - 10:52 PM IST

BTech Admission 2025 Live: JEE Mains, SRMJEEE, MET registrations underway; MHT CET syllabus updates

November 17, 2024 - 09:11 PM IST

JEE Mains 2025 session 1 registration deadline on November 22; apply on jeemain.nta.nic.in

November 17, 2024 - 03:28 PM IST

BTech Admissions 2025 Live: JEE Mains, SRMJEE, VITEEE dates out; AEEE, MET registrations underway

November 15, 2024 - 11:12 AM IST

Centre issues coaching guidelines, prohibits centres from using false claims like '100% selection'

November 13, 2024 - 06:45 PM IST

BTech Admissions 2025: JEE Mains registration underway; updates on state engineering exams

November 13, 2024 - 11:45 AM IST

BTech Admissions 2025: JEE Mains, VITEEE, SRMJEE exam dates announced

November 12, 2024 - 10:27 PM IST

Download Careers360 App

All this at the convenience of your phone

Regular Exam Updates
Best College Recommendations
College & Rank predictors
Detailed Books and Sample Papers
Question and Answers

Scan and download the app

OR

Joint Entrance Examination (Main)

JEE Main 2025 Sample Papers