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 :

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) to (x, y) in the ratio 1 : 3. Then the locus of P is

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 : (1) x^2=""y (2) y^2=""x (3) y^2=""2x (4) x^2=""2y

The point P(x,y) divide the line segment joining A(2,2) and B(3,4) in the ratio 1.2 then x+y is

Let P be a point on the parabola y^(2) - 2y - 4x+5=0 , such that the tangent on the parabola at P intersects the directrix at point Q. Let R be the point that divides the line segment PQ externally in the ratio 1/2 : 1. Find the locus of R.

The point P divides the join of (2,1) and (-3,6) in the ratio 2:3. Does P lie on the line x-5y+15=0?

Let A(alpha,0) and B(0,beta) be the points on the line 5x+7y=50 .Let the point divide the line segment "AB" internally in the ratio "7:3" .Let 3x-25=0 be a directrix of the ellipse E:(x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and the corresponding focus be "S" .If from "S", the perpendicular on the "x" -axis passes through "P" ,then the length of the latus rectum of "E" is equal to,

If P is point on the parabola y ^(2) =8x and A is the point (1,0), then the locus of the mid point of the line segment AP is

Let P be a point on x^2 = 4y . The segment joining A (0,-1) and P is divided by point Q in the ratio 1:2, then locus of point Q is