If AOB and COD are two straight lines which bisect one another at right angles, show that the locus of a point P which moves so that `PAxxPB=PCxxPD` is a hyperbola.
Find its eccentricity.

If A O Ba n dC O D are two straight lines which bisect one another at right angles, show that the locus of a points P which moves so that P AxP B=P CxP D is a hyperbola. Find its eccentricity.

Find the locus of a point which divides so that the sum of its distances from (-4,0) and (4,0) is 10 units.

Find the locus of a point which moves such thet its distance from the x axis is twice the distance from y axis.

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.

A rod of length 1.2 m moves with its ends always touching the coordinate axes. The locus of a point Pon the rod, which is 0.3 m from the end in contact with x-axis is an ellipse. Find the eccentricity.

Find the locus of the point at which two given portions of the straight line subtend equal angle.

A straight line segment of length/moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio 1:2

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry I_1 and I_2 currents, respectively. Point P is lying at distance d from O along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

A series of chords are drawn so that their projections on the straight line, which is inclined at an angle a to the axis, are of constant length cdot Prove that the locus of their middle point is the curve. (y^2-4a x)(ycosalpha+2asinalpha)^2+a^2c^2=0.