if the line (x-y+1) + k(y-2k+4) =0 makes equal intercepts on the axes

1.	if the line (x-y+1) + k(y-2k+4) =0 makes equal intercepts on the axes . Then what is the value of k ?
Answer» $\textbf{Given:}$ $\text{<klux>EQUATION</klux> of the <klux>LINE</klux> is (x-y+1)+k(y-2k+4)=0}$ $\textbf{To find:}$ $\text{The value of k}$ $\textbf{Solution:}$ $\text{Consider,}$ $(x-y+1)+k(y-2k+4)=0$ $x+(k-1)y-2k^2+4k+1=0$ $x+(k-1)y=2k^2-4k-1$ $\text{Divide both sides by $2k^2-4k-1$}$ $\dfrac{x}{2k^2-4k-1}+\dfrac{(k-1)y}{2k^2-4k-1}=1$ $\dfrac{x}{2k^2-4k-1}+\dfrac{y}{\dfrac{2k^2-4k-1}{k-1}}=1$ $\text{Comparing this with}$ $\bf\,\dfrac{x}{a}+\dfrac{y}{<klux>B</klux>}=1$ $\text{we get}$ $\text{x-<klux>INTERCEPT</klux>,}\;a=2k^2-4k-1$ $\text{y-intercept,}\;b=\dfrac{2k^2-4k-1}{k-1}$ $\text{But,}\;a=b$ $2k^2-4k-1=\dfrac{2k^2-4k-1}{k-1}$ $1=\dfrac{1}{k-1}$ $k-1=1$ $\implies\boxed{\bf\,k=2}$ $\therefore\textbf{The value of k is 2}$ Find more: Equation of the line having intercepts a,b on the AXES such that a+b=5 ,ab=6 is brainly.in/question/8573548 Find the equation of line passing through the point (5,6) and making equal intercept on x & y axis brainly.in/question/13417461