If `P` is any point on the plane `l x+m y+n z=pa n dQ` is a point on the line `O P` such that `O PdotO Q=p^2` , then find the locus of the point `Qdot`

If R is any point on the x-axis and Q is any point on they y-axis and P is a variable point on RQ with RP=b, PQ=a, then find the equation of locus of P.

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

From any point on the line y=x+4, tangents are drawn to the auxiliary circle of the ellipse x^2+4y^2=4 . If P and Q are the points of contact and Aa n dB are the corresponding points of Pa n dQ on he ellipse, respectively, then find the locus of the midpoint of A Bdot

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot

Two points P(a,0) and Q(-a,0) are given. R is a variable point on one side of the line P Q such that /_R P Q-/_R Q P is a positive constant 2alphadot Find the locus of the point Rdot

Let O be the vertex and Q be any point on the parabola, x^2=""8y . It the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

A circle with center at the origin and radius equal to a meets the axis of x at Aa n dBdotP(alpha) and Q(beta) are two points on the circle so that alpha-beta=2y , where gamma is a constant. Find the locus of the point of intersection of A P and B Qdot