Question

find the equation of line passing through the point of intersection of line x-5y-17=0 and 8x+3y-7=0 and which makes equal intercept on the coordinate axis

Answer 1

$\textbf{Given:}$

$\textsf{Lines are x-5y-17=0 and 8x+3y-7=0}$

$\textbf{To find:}$

$\textsf{The equation of  the line passing through the point of}$

$\textsf{intersection of the given two lines}$

$\textbf{Solution:}$

$\textsf{First we find out point of intersection of the given lines}$

$\mathsf{x-5y-17=0}$

$\mathsf{8x+3y-7=0}$

$\textsf{By cross multiplication rule,}$

$\mathsf{\dfrac{x}{35+51}=\dfrac{y}{-136+7}=\dfrac{1}{3+40}}$

$\mathsf{\dfrac{x}{96}=\dfrac{y}{-129}=\dfrac{1}{43}}$

$\mathsf{x=\dfrac{96}{43}=2}$

$\mathsf{y=\dfrac{-129}{51}=-3}$

$\textsf{The point of intersection is (2,-3)}$

$\textsf{Equation of the line passing through point of intersection}$

$\textsf{of given lines in intercept form can be written as}$

$\mathsf{\dfrac{x}{a}+\dfrac{y}{b}=1}$

$\mathsf{But\;a=b}$

$\mathsf{\dfrac{x}{a}+\dfrac{y}{a}=1}$

$\mathsf{x+y=a}$

$\textsf{This line passes through (2,-3)}$

$\mathsf{2-3=a}$

$\mathsf{a=-1}$

$\therefore\textsf{The required line is x+y+1=0}$

$\textbf{Find more:}$

Find the equation of line passing through the point (5,6) and making equal intercept on x & y axis​

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If the line (x-y+1) + k(y-2k+4) =0 makes equal intercepts on the axes . Then what is the value of k

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Answer 2

$\underline\texttt{☆Given:-}$

$\textsf{Lines are x-5y-17=0 and 8x+3y-7=0}$

$\underline\texttt{☆To find:-}$

$\textsf{The equation of  the line passing through the point of}$

$\textsf{intersection of the given two lines}$

$\underline\texttt{☆Solution:}$

$\textsf{First we find out point of intersection of the given lines}$

$\mathsf{x-5y-17=0}$

$\mathsf{8x+3y-7=0}$

$\underline\textsf{☆By cross multiplication rule,}$

$\mathsf{\dfrac{x}{35+51}=\dfrac{y}{-136+7}=\dfrac{1}{3+40}}$

$\mathsf{\dfrac{x}{96}=\dfrac{y}{-129}=\dfrac{1}{43}}$

$\mathsf{x=\dfrac{96}{43}=2}$

$\mathsf{y=\dfrac{-129}{51}=-3}$

$\textsf{The point of intersection is (2,-3)}$

$\textsf{Equation of the line passing through point of intersection}$

$\textsf{of given lines in intercept form can be written as}$

$\mathsf{\dfrac{x}{a}+\dfrac{y}{b}=1}$

$\mathsf{But\;a=b}$

$\mathsf{\dfrac{x}{a}+\dfrac{y}{a}=1}$

$\mathsf{x+y=a}$

$\textsf{This line passes through (2,-3)}$

$\mathsf{2-3=a}$

$\mathsf{a=-1}$

$\therefore\underline\textsf{☆The required line is x+y+1=0}$

$\small{\textbf{\textsf{{\color{navy}\:{☆Hope}}\:{\purple{it}}\:{\pink{helps}}\:{\color{pink}{you!!☆}}}}}$