Trigonometric EquationHard

Question

Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is

Options

A.x2 + y2 =
B.x2 + y2 = 4p2
C.
D.

Solution

       
Equation of AB is x cos α + y sin α = p ⇒ = 1 ⇒
So co-ordinates of A and B are and ; So coordinates of mid point of AB are
= (x1, y1)(let) ; x1 = & y1 = ;
⇒   cosα = p/2x1 and sin α = p/2y1 ; cos2α + sin2α = 1 ⇒
Locus of (X1, y1) is

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