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.
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).
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