Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The shortest distance between the parabola  and the circle <img alt="

The shortest distance between the parabola \mathrm{y^2=4 x} and the circle \mathrm{x^2+y^2+6 x-12 y+20=0}  is 

Option: 1

0


Option: 2

1


Option: 3

4\sqrt{2}-5


Option: 4

4\sqrt{2}+5


Answers (1)

best_answer

Normal at \mathrm{\left(m^2, 2 m\right)} to the parabola is \mathrm{ y=m x-2 m-m^3}.
Since this is normal to the circle also.
\mathrm{\therefore}  It passes through the centre of the circle

\mathrm{\begin{aligned} & \mathrm{\Rightarrow \quad 6=-3 m-2 m-m^3 \Rightarrow m=-1} \\ & \therefore \mathrm{A} \equiv(1,2) \end{aligned} }
Q Shortest distance between parabola and circle will be along the common normal

\mathrm{\Rightarrow} Shortest distance \mathrm{=A C=A B-B C=4 \sqrt{2}-5}.

Posted by

qnaprep

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

Top engineering colleges in Maharashtra with NIRF rankings; MHT CET, JEE Main, JEE Adv scores valid
anam-khan

JEE Mains 2025 Session 2 Registration: Class 12, PU, NDA, NIOS, IB students eligible; list of qualifying exams
anam-khan

JEE Mains 2025 Cut-offs: What is expected? previous years' passing marks

Latest Question