Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the point on the curve   nearest to the point  <img a

If the point on the curve  \mathrm {y^2=6 x,} nearest to the point  \mathrm {(3,3 / 2)}  is  \mathrm {(\alpha, \beta)} , then  \mathrm {2(\alpha+\beta)}  is equal to_____

Option: 1

8


Option: 2

6


Option: 3

7


Option: 4

9


Answers (1)

We have, \mathrm {y^2=6 x} 
Minimum distance is along the normal at point

\mathrm {P \equiv\left(\frac{3}{2} t^2, 3 t\right)}

Normal at point  \mathrm {P \: \: is\: \: t x+y=3 t+\frac{3}{2} t^3} ,

which passes through the point \mathrm {\left(3, \frac{3}{2}\right).}

\begin{aligned} & \therefore \quad 3 t+\frac{3}{2}=3 t+\frac{3}{2} t^3 \Rightarrow t^3=1 \Rightarrow t=1 \\ & \therefore \quad P \equiv\left(\frac{3}{2}, 3\right) \\ & \alpha+\beta=\frac{3}{2}+3=\frac{9}{2} \Rightarrow 2(\alpha+\beta)=9 . \end{aligned}

Posted by

Sumit Saini

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

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question