Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The equation of a line inclined at an angle to the axis <img alt="\mathrm{X}" src="https:

The equation of a line inclined at an angle \frac{\pi}{4} to the axis \mathrm{X}, such that the two circles \mathrm{x^{2}+y^{2}=4, x^{2}+y^{2}-10 x-14 y+65=0} intercept equal lengths on it, is

Option: 1

\mathrm{2 x-2 y-3=0}


Option: 2

\mathrm{2 x-2 y+3=0}


Option: 3

\mathrm{x-y+6=0}


Option: 4

\mathrm{x-y-6=0}


Answers (1)

best_answer

 Let equation of line be \mathrm{y=x+c}

\mathrm{\mathrm{y}-\mathrm{x}=\mathrm{c}}
perpendicular from (0,0) on (1) is \left|\frac{-\mathrm{c}}{\sqrt{2}}\right|=\frac{\mathrm{c}}{\sqrt{2}}

\mathrm{In\, \triangle \mathrm{AON}, \quad \sqrt{2^{2}-\left(\frac{\mathrm{c}}{\sqrt{2}}\right)^{2}}=\mathrm{AN}}

\mathrm{and\: in \: \triangle \mathrm{CPM}, \sqrt{3^{2}-2-\frac{\mathrm{c}}{\sqrt{2}}}=\mathrm{CM}}
perpendicular from \mathrm{(5,7)} on line \mathrm{y-x=c=\frac{2-c}{\sqrt{2}}\, }



\mathrm{Given \, \mathrm{AN}=\mathrm{CM}=4-\frac{\mathrm{c}^{2}}{2}=9-\frac{(2-\mathrm{c})^{2}}{2} \Rightarrow \mathrm{c}=-\frac{3}{2} }

\mathrm{\therefore \quad \text{equation of line }y=x-\frac{3}{2} \, of \, 2 x-2 y-3=0 }

Posted by

Pankaj

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question