Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Two circles <img alt="\mathrm{x^2+y^2-10 x+16=0 \text { and } x^2+y^2=r^2{}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%5E2&plus;y%5E2-10%20x&plus;16%3D0%20%5Ct

Two circles \mathrm{x^2+y^2-10 x+16=0 \text { and } x^2+y^2=r^2{}  intersect each other at two distinct points if

Option: 1

\mathrm{r<2}


Option: 2

\mathrm{r>8}


Option: 3

\mathrm{2<r<8}


Option: 4

none of these


Answers (1)

best_answer

For circle \mathrm{x^2+y^2-10 x+16} , the centre is  \mathrm{C_2(5,0)} and \mathrm{r_2=\text { radius }=\sqrt{25-16}=3}

For circle \mathrm{x^2+y^2=r^2} , , the centre is  \mathrm{C_1(0,0)} and radius = r

The circles intersect at two distinct points if the distance between the centre is greater than the difference between their radii and less than the sum of their radii.

\mathrm{\begin{aligned} & \Rightarrow|3-r|<C_1 C_2<3+r \\ & \text { Or }|3-r|<5<3+r \end{aligned}}

\mathrm{r-3<5 \text { or } r<8}

Posted by

Irshad Anwar

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 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus
anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question