A line through $$P(1$$, $$2)$$ is such that it makes unequal intercepts on the axes, and the intercept between the axes is trisected at P, an equation of the line is

Question

A line through  $$P(1$$, $$2)$$ is such that it makes unequal intercepts on the axes, and the intercept between the axes is trisected at P, an equation of the line is

Infinity Learn · Accepted Answer

Let the equation of the line be $$xa+yb=1$$,which meets $$x-axis$$ at A (a$$, $$0) and $$y-axis$$ at B (0$$, $$b). Thenthe coordinates of the points which divide AB in the ratio $$1$$ : $$2$$ and $$2$$ : $$1$$ are respectively $$2a3$$,$$b3$$ and $$a3$$,$$2b3$$ Now if $$2a3$$,$$b3$$ represents P (1$$, $$2) then $$a=3/2$$,$$b=6$$ and the required equation of the line is $$2x3+y6=1$$⇒$$4x+y=6$$ which is given in (b) If $$a3$$,$$2b3$$ represents P (1$$, $$2) then a $$=$$ b $$=$$ $$3and$$ the equation of the line is x $$+$$ y $$=$$ $$3$$ which makes equal intercepts on the axes and so we do not consider this.

A line through $P (1, 2)$ is such that it makes unequal intercepts on the axes, and the intercept between the axes is trisected at P, an equation of the line is

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A line through P(1, 2) is such that it makes unequal intercepts on the axes, and the intercept between the axes is trisected at P, an equation of the line is

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A line through $P (1, 2)$ is such that it makes unequal intercepts on the axes, and the intercept between the axes is trisected at P, an equation of the line is