Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If tangent at to the circle <img alt="\mathrm{x^2+y^2=5}" src="https://entrancecorner.oncodecogs.com/gif.latex?

If tangent at (1,2) to the circle \mathrm{x^2+y^2=5} intersects the circle \mathrm{x^2+y^2=9} at \mathrm{A \: and\: B} and tangents at \mathrm{A \: and\: B} to the second circle meet at point \mathrm{C}, then the coordinates of \mathrm{C}  are
 

Option: 1

\left ( 4,5 \right )


Option: 2

\left(\frac{9}{15}, \frac{18}{5}\right)



 


Option: 3

(4,-5)


Option: 4

\left(\frac{9}{5}, \frac{18}{5}\right)


Answers (1)

best_answer

tangent at (1,2) is given by

\mathrm{x+2 y-5=0}
Let point \mathrm{C} be \mathrm{(h,k)}. Then this tangent will be chord of contact of this point w.r.t. the IInd circle, whose equation will be \mathrm{x h+y k-9=0}. Both are same lines so

\mathrm{ \frac{\mathrm{h}}{1}=\frac{\mathrm{k}}{2}=\frac{9}{5} \Rightarrow(\mathrm{h}, \mathrm{k})=\left(\frac{9}{5}, \frac{18}{5}\right) }

Hence option 4 is correct.
 

Posted by

jitender.kumar

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: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question