Exercise - 6.1

. Find the locus of P , if for all values of α , the co-ordinates of a moving point P is ( i ) ( cos α , sin α ) ( ii ) ( cos α , sin α ) . . Find the locus of a point P that moves at a constant distant of (i) two units from the x -axis (ii) three units from the y -axis.

. If θ is a parameter, find the equation of the locus of a moving point, whose coordinates are x = a cos θ , y = a sin θ . . Find the value of k and b , if the points P ( − , ) and Q ( , b ) lie on the locus of x − x + ky = .

. A straight rod of length units slides with its ends A and B always on the x and y axes respectively. Find the locus of the mid point of the line segment AB . Find the equation of the locus of a point such that the sum of the squares of the distance from the points ( , ) , ( , − ) is equal to .

Find the equation of the locus of the point P such that the line segment AB , joining the points A ( , − ) and B ( , − ) , subtends a right angle at P . . If O is origin and R is a variable point on y = x , then find the equation of the locus of the mid-point of the line segment OR . .

The coordinates of a moving point P are a (cosec θ + sin θ ) , b (cosec θ − sin θ ) , where θ is a variable parameter. Show that the equation of the locus P is b x − a y = a b . . If P ( , − ) is a given point and Q is a point on x + y = , then find the equations of the locus of the mid-point of PQ .