Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • From the point N(5,2) normals are drawn to the parabola to meet the curve at A and

From the point N(5,2) normals are drawn to the parabola \mathrm{y^2=4 x} to meet the curve at A and B. If the tangents to the curve at A and B meet at the point T, then \mathrm{T N^2} is equal to

Option: 1

50


Option: 2

60


Option: 3

40


Option: 4

70


Answers (1)

best_answer

\mathrm{\text { The normal at } t \text { is } x t+y=t^3+2 t \text {. }}

It passes through N(5, 2).

\mathrm{\therefore t^3-3 t-2=0, \text { Solving } t=-1,-1,2}

\mathrm{\text { The points are given by }\left(t^2, 2 t\right)}

A ≡ (1, –2), B ≡ (4, 4)
The tangents at A and B meet at

\mathrm{T\left(t_1 t_2, t_1+t_2\right) \text { or } T \equiv(-2,1), T N^2=(5+2)^2+(2-1)^2=50 \text {. }}

Posted by

Gunjita

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

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

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question