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 P.O Q=p^2` , then find the locus of the point `Qdot`

If P is a point (x, y) on the line y= -3x such that P and Q(3, 4) are on opposite sides of the line 3x-4y=8 , then :

The normal at a point P on the ellipse x^(2)+4y^(2)=16 meets the x-axisat Q. If M is the mid-point of the line segment PQ, then the locus of M intersects the latus-rectum of the given ellipse at the points :

A=(-9,0) and B=(-1,0) are two points. If P(x, y) is a point such that 3 P B=P A , then the locus of P is

If the point P(a, b) lies on the line 3 x+2 y=13 and the point Q(b, a) lies on the line 4 x-y=5 , then the equation of the line P Q is

Let O be the origin and A be a point on the curve y^(2)=4 x . Then the locus of the midpoint of O A is

Let O be the vertex and Q be any point on the parabola x^(2)=8y if the point p divides the line segement OQ internally in the ratio 1:3 then the locus of P is

P is any point on the ellipse 9x^2 + 36y^2 = 324 whose foci are S and S' , SP + S'P =

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.

Show that the relation R in the set A of points in a plane given by R = {(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

Suppose A, B are two points on 2 x-y+3=0 and P(1,2) is such that P A=P B , then the mid point of A B is