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Q.
The equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point $(2,3)$ is
Straight Lines
Solution:
Equation of line in intercept form is
$\frac{x}{a}+\frac{y}{b}=1 .....$(i)
Since, the line makes equal intercepts on the axes i.e.,
$a =b $
$\therefore $ From Eq. (i), $ \frac{x}{a}+\frac{y}{a} =1$
$\Rightarrow x+y =a......$(ii)
Line (ii) passes through the point $(2,3)$, it will satisfy the line (ii).
$2+3=a \Rightarrow a=5$
Put the value of $a$ in Eq. (ii), we get
$x+y=5$