Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If a circle    touches at the point  <img alt="\mat

If a circle  \mathrm{S(x, y)=0}  touches at the point  \mathrm{(2,3) } of the line \mathrm{ x+y=5 }  and \mathrm{S(1,2)=0}, then radius of

such circle

Option: 1

2units


Option: 2

4units


Option: 3

\mathrm{\frac{1}{2} \text { units }}


Option: 4

\mathrm{\frac{1}{\sqrt{2}} units}


Answers (1)

best_answer

Desired equation of the circle is

\mathrm{\begin{aligned} & (x-2)^2+(y-3)^2+\lambda(x+y-5)=0 \\\\ & 1+1+\lambda(1+2-5)=0 \Rightarrow \lambda=1 \\\\ & x^2-4 x+4+y^2-6 y+9+x+y-5=0 \Rightarrow x^2+y^2-3 x-5 y+8=0 \\\\ & \left(x^2+\frac{3}{2}\right)^2+\left(y-\frac{5}{2}\right)^2=-8+\frac{25}{4}+\frac{9}{4}=\frac{2}{4}=\frac{1}{2} . \end{aligned}}

Hence (c) is correct answer.

Posted by

avinash.dongre

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: NIT Rourkela records higher closing ranks in CSE, ECE, AI; core engineering branches stable
anam-khan

JEE Main 2026: IIT Delhi’s CSE, EE most opted; last 2 year’s closing ranks for all categories
anam-khan

Must provide CBSE 11th registration numbers to JEE Mains aspirants, board tells schools

Latest Question