Question

Find the equation of locus of the trisection point of the portion of the line x cos alpha + y sin alpha = p intercepted between the coordinate axes.

Answer 1

Thus the locus equation is 1/x^2 + 1/y^2 = 4 / p^2

Step-by-step explanation:

The equation of locus can be found as;

p sec α / 2 = h    , p cosec α / 2 = x

2 h / p = sec α     , 2 x / p = cosec α

p / 2 h = cos α    , p / 2 x  = sin α

Now taking square of both equation and then adding them will give us;

p^2 / 4 h^2 + p^2 / 4 x^2 |   p (h , x )

1 / 4 x^2 + 1 / 4y^2 = 1/p^2

1/x^2 + 1/y^2 = 4 / p^2

Thus the locus equation is 1/x^2 + 1/y^2 = 4 / p^2