`B` is a variable point on`y^2 = 4ax`. The line `OB` (`O` : origin) is extended to the point `M` such that `OM= lambda0B`. The locus of `M `is

A-=(-4,0) ,B-=(4,0). M and N are the variable point of the y-axis such that M lies below N and MN=4. Lines AM and BN intersect at P. The locus of P is

If O is the origin and Q is a variable point on y^(2)=x* Find the locus of the mid point of OQ

If O is the origin and Q is a variable, point on x^(2)=4y , find the locus of the mid-point of OQ.

If O is the origin and Q is a variable point on y^2=xdot Find the locus of the mid point of \ O Qdot

Two fixed point A and B are taken on the cordinate axes such that OA = a and OB = b. Two variable points A' and B' are taken on the same axes such that OA'+OB' = OA + OB. Find the locus of the point of intersection of AB' and A'B.

If O is origin and R is a variable point on y^(2)=4x , then find the equation of the locus of the mid-point of the line segment OR.

If O is origin and R is a variable point on y^2=4x , then find the equation of the locus of the mid-point of the line segmet OR .

If O is origin and R is a variable point on y^2=2x , then find the equation of the locus of the mid-point of the line segment OR.