Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A line  through the point <img alt="\mathrm{A\left ( 2,-7 \right )

A line \mathrm{4x+y=1} through the point \mathrm{A\left ( 2,-7 \right )} meets the line \mathrm{BC}, whose equation is \mathrm{3 x-4 y+1=0} at the point \mathrm{B}.  Find the equation to the line \mathrm{AC} , so that \mathrm{AB=AC.}

Option: 1

\mathrm{21 x+79 y-519=0}


Option: 2

\mathrm{52 x+89 y-519=0}


Option: 3

\mathrm{52 x+89 y+519=0}


Option: 4

\mathrm{21 x+79 y+519=0}


Answers (1)

best_answer

Equation of line \mathrm{AB} is \mathrm{4x + y = 1.}
Its slope \mathrm{= -4.}
Slope of line \mathrm{3 x-4 y+1=0 \text { is } 3 / 4.}
If \mathrm{\alpha } is angle \mathrm{ABC }, then    \mathrm{\tan \alpha=\frac{-4-3 / 4}{1+(-4) \cdot(3 / 4)}=\frac{19}{8} }.              
Given that \mathrm{AB=AC}

Hence the given line passes through the point \mathrm{\left ( a/c,b/c \right )}, which is a fixed point since \mathrm{a,b,c} are constants.
\mathrm{\therefore \angle \mathrm{ACB}=\angle \mathrm{ABC}=\alpha}
If the slope of \mathrm{AC} is \mathrm{m}, then \mathrm{\tan \alpha=\frac{19}{8}= \pm \frac{m-3 / 4}{1+m \cdot(3 / 4)}}
or \mathrm{19(4+3 m)= \pm 8(4 m-3) \Rightarrow m=-4 \text { or }-52 / 89}
But \mathrm{-4} is the slopeof line \mathrm{AB},                  \mathrm{\Rightarrow \therefore } slope of \mathrm{AC}
\mathrm{=m=-52 / 89} 
Hence the equation of line \mathrm{AC} which passes through \mathrm{A\left ( 2,-7 \right )} and has slope
\mathrm{\begin{aligned} & \mathrm{m}=-52 / 89 \text { is } \quad \mathrm{y}+7=\left(-\frac{52}{89}\right)(\mathrm{x}-2) \\ & \text { or } \quad 52 \mathrm{x}+89 \mathrm{y}+519=0 \end{aligned}}

Posted by

manish painkra

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