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Question

Find the equation of the straight line which passes through the point P(2, 6) and cuts the coordinate axes at the point A and B respectively so that APBP=23.


Solution

The equation of the line with intercepts

a and b is xa+yb=1

Since, the line meets the coordinate axes at A and B, the coordinates of A and B are A (a, 0) and B (0, b).

Given:AP:BP=2:3

Here, P=(2, 6)

 2=2×0+3×a2+3, 6=2×b+3×02+3

 3a=10, 2b=30

 a=103, b=15

Thus, the equation of the line is

x103+y15=1

 3x10+y15=1

 9x+2y=30


Mathematics
RD Sharma
Standard XI

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