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Question

A straight line passes through the point (α, β) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is x2 α+y2 β=1.


Solution

The equation of the line with interceptsa and b isxa+yb=1This line intersects the axes at A (a, 0) and B (0, b)Here, (α, β) is the midpoint of AB α=a+02, β=0+b2 a=2α, b=2βHence, the equation of the line isx2α+y2β=1


Mathematics
RD Sharma
Standard XI

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