The end points P and Q of a rod PQ having length 8 unit slide along the lines y = 2 and x = 4 respectively. Find the equation of the locus of the mid point of the rod.

The ends A and B of a rod AB of length 8 unit slide along the lines y=2 and x=4 respectively. Find the equation to the locus of the mid point of the rod.

The end’ points of a rod having length l are moving a long with two straight line which are perpendicular toeach othcr. Find the equation -of the locus of the point which divides the rod are in ratio 2:1.

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

A striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The straight line PQ is perpendicular to AB and intersect the x and y-axes at P adn Q respectively. Find the eqution to the locus of the point of intersection of the line AQ and BP.

A rod PQ of length 16 units moves with its ends P and Q always touching x-axis and y-axis respectively. Determine the equation of the locus of a point K on PQ which is always at a distance of 4 unit from P.

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

bar(PQ) is a double ordinate of the parabola y^2=4ax ,find the equation to the locus of its point of trisection.

A circle of radius r passes through the origin and intersects the x-axis and y-axis at P and Q respectively. Show that the equation to the locus of the foot of the perpendicular drawn form the origin upon the line segment bar (PQ) is (x^(2)+y^(2))^(3)=4r^(2)x^(2)y^(2) .

Two rods of lengths a and b slide along the x- and y-axis , respectively, in such a manner that their ends are concyclic. Find the locus of the center of the circle passing through the endpoints.

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is