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) 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) = 8 y . If the point P divides the line segments OQ internally 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 . IF the point P divides the line segment OQ internally in the ratio 1:3 , then the locus of P is

A is a point on the circle x^(2)+y^(2)=36 . Find the locus of the point P which divides the ordinate bar (AN) internally in the ratio 2:1 .

If the line x+y =1 is a tangent to the parabola y^(2)-y +x=0 , then the point of contact is-

Let P be the midpoint of a chord joining the vertex of the parabola y^(2) = 8x to another point on it . Then locus of P .

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=0

Let P be the point (1,0) and Q a point on the parabola y^(2) =8x, then the locus of mid-point of bar(PQ is-

If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is

Let the foci of the ellipse (x^(2))/(9) + y^(2) = 1 subtend a right angle at a point P . Then the locus of P is _

Let P and Q be the points on the prabola y^(2) = 4x so that the line segment PQ subtends right at the vertex . If PQ intersects the axis of the parabola at R , then the distance of the vertex from R is _