Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If two different tangents of are the normals to <img alt="\mathrm{x^{2}=4by

If two different tangents of \mathrm{y^{2}=4 x} are the normals to \mathrm{x^{2}=4by}, then

Option: 1

\mathrm{|b|>\frac{1}{2 \sqrt{2}}}


Option: 2

\mathrm{|b|<\frac{1}{2 \sqrt{2}}}


Option: 3

\mathrm{|b|>\frac{1}{\sqrt{2}}}


Option: 4

\mathrm{|b|<\frac{1}{\sqrt{2}}}


Answers (1)

best_answer

Tangent to \mathrm{y^{2}=4 x} in terms of \mathrm{m} is

\mathrm{y=m x+\frac{1}{m}}.
Normal to \mathrm{x^{2}=4by} in terms of \mathrm{m} is
\mathrm{y=m x+2 b+\frac{b}{m^{2}}}.

If these are same lines, then
\mathrm{\frac{1}{m}=2 b+\frac{b}{m^{2}}}
\mathrm{\Rightarrow \quad 2 b m^{2}-m+b=0}

For two different tangents, we must have
\begin{gathered} 1-8 b^{2}>0 \\ \Rightarrow \quad|b|<\frac{1}{\sqrt{8}} \end{gathered}

Posted by

mansi

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