PN is any ordinate of the parabola `y^(2) = 4ax` , the point M divides PN in the ratio m: n . Find the locus of M .

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

overline(PQ) is a double ordinate of the parabola y^(2) = 4ax ,find the equation to the locus of its point of trisection .

PQ is a double ordinate of a parabola y^(2)=4ax. Find the locus of its points of trisection.

Let (x,y) be any point on the parabola y^(2)=4x. Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :

The abscissa of any points on the parabola y^(2)=4ax are in the ratio mu:1. If the locus of the point of intersection at these two points is y^(2)=(mu^((1)/(lambda))+mu^(-(1)/(lambda)))^(2) ax.Then find lambda

the abscissae of any two points on the parabola y^(2)=4ax are in the ratio u:1. prove that the locus of the point of intersection of tangents at these points is y^(2)=(u^((1)/(4))+u^(-((1)/(4))))^(2)ax

The ordinates of points P and Q on the parabola y^2 = 12x are in the ratio 1 : 2. Find the locus of the point of intersection of the normals to the parabola at P and Q.

Let (x,y) be any point on the parabola y^2 = 4x . Let P be the point that divides the line segment from (0,0) and (x,y) n the ratio 1:3. Then the locus of P is :