Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A circle touches both the y-axis and the line . Then the locus of its center i

A circle touches both the y-axis and the line \mathrm{x+y=0}. Then the locus of its center is :

 

Option: 1

\mathrm{y=\sqrt{2x}}


Option: 2

\mathrm{x=\sqrt{2y}}


Option: 3

\mathrm{y^{2}-x^{2}=2y}


Option: 4

\mathrm{x^{2}-y^{2}=2xy}


Answers (1)

best_answer

 

To find locus, let centre be \mathrm{h,k}\\

      \mathrm{|OM|=|ON|}\\ distance

\Rightarrow \mathrm{|h|=\frac{|h+k|}{\sqrt{2}}}\\

Squaring both side we get

\Rightarrow \mathrm{2h^{2}=\left ( h+k \right )^{2}}\\

\Rightarrow \mathrm{2h^{2}=h^{2}+k^{2}+2kh}\\

      \mathrm{2x^{2}=x^{2}+y^{2}+2xy}\\

\Rightarrow \mathrm{x^{2}-y^{2}-2xy=0}

Hence the correct answer is option 4

Posted by

Sanket Gandhi

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 2025: BTech ECE cut-offs went up for IIIT Allahabad, Tiruchirappalli last year; closing ranks
anam-khan

JEE Main session 2 application closes at 9 pm; NTA says ‘no further extension’ of registration last date
anam-khan

JEE Mains 2025 session 2 application correction facility on February 27, 28; registration ends tomorrow

Latest Question