Let us choose the intersection point of the given lines as the origin and their angular bisector as the x-axis. Equation of the two lines will then be

y = mx and y = – mx

where m = tan α .

Let P(h, k) be the point whose locus is to be found,

then according to the given condition

PA 2 + PB 2 = constant ⇒ + = c (c is a constant)

i.e. 2(k 2 + m 2 h 2 ) = c(1 + m 2 )

Therefore, the locus of P is + = 1 where a 2 = and b 2 =

If α < π /4, then m < 1, then a 2 > b 2 , and hence eccentricity = = =

If α > π /4, then m > 1,then a 2 < b 2 , and hence eccentricity= = = .

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