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

Find the equation of the locus of a point, the tangents from which to the ellipse 3x^2+5y^2=15 are at right angles.

Find the equation of locus of the point P,if the points A(1,2),B(3,4) are at equal distance from P.

Find the equation of the locus of a point, the tangents from which to the parabola y^2=18x are such that sum of their slope is -3.

Find the coordinates of the point on Y-axis which is equidistant from the points M(6,5) and point N(-4,3).

The abscissa of the point on the curve ay^2 = x^3 , the normal at which cuts off equal intercepts from the coordinate axes is

A rod of length l is rotated about its one end, perpendicular to a magnetic field of induction B What is the e.m.f induced in the rod

A straight horizontal conducting rod of length 0.45 m and mass 60 g is suspended by two vertical wires at its ends. A current of 5.0 A is set up in the rod through the wires. What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before ? (Ignore the mass of the wires) g = 9.8 ms^-2

A variable circle passes through the fixed point A(p,q) and touches X-axis. The locus of the other end of the diameter through A is