A rod of length 12 cm moves with its ends alwaystouching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

A rod of length 12 cm moves with its ends always touching the coordinates axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end-in contact with x-axis.

Find the locus of a point which moves such that its distance from the origin is three times its distance from x-axis.

Find the equation of the locus of a point which moves so that the difference of its distances from the points (3, 0) and (-3, 0) is 4 units.

The ends of a rod of length l move on two mutually perpendicular lines. Find the locus of the point on the rod which divides it in the ratio 1 : 2.

A rod AB of length 15 cm rests in between two co-ordinate axes in such a way that the end point A lies on the x-axis and end point B lies on y-axis. A point P (x, y) is taken on the rod in such a way that AP = 6 cm. Prove that the locus of P is an ellipse.

If a rod AB of length 2 units slides on coordinate axes in the first quadrant. An equilateral triangle ABC is completed with C on the side away from O. Then, locus of C is

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is

The angle between a pair of tangents from a point P to the circle x^2 + y^2 = 25 is pi/3 . Find the equation of the locus of the point P.

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

Find the equation of the circle, which touches the axis of x at a distance 3 from the Origin and intercepts a length 6 on the axis of y.