`PQ` is a chord of a parabola normala at `P.A.` is the vertex and through `P`, a lineis drawn parallel to `AQ` meeting the axis in in `R`. Show that `AR` is double the focal distance of `P`.

PQ is a normal chord of the parabola y^2 =4ax at P, A being the vertex of the parabola. Through P, a line is drawn parallel to AQ meeting the x-axis at R. Then the line length of AR is (A) equal to the length of the latus rectum (B)equal to the focal distance of the point P (C) equal to twice the focal distance of the point P (D) equal to the distance of the point P from the directrix.

PQ is a chord of parabola normal at P.Q. is the vertex and r the focus distance of P . If the line through P , parallel to AQ meets the axis in R , then AR= (A) r (B) 2r (C) 3r (D) r/2

AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projecton of BC on the axis of the parabola is

Show that all chords of a parabola which subtend a right angle at the vertex pass through a fixed point on the axis of the curve.

PSQ is a focal chord of the parabola y^2=8x. If\ S P=6, then write SQ.

PQ is a double ordinate of the parabola y^2 = 4ax . If the normal at P intersect the line passing through Q and parallel to axis of x at G, then locus of G is a parabola with -

PSQ is a focal chord of a parabola whose focus is S and vertex is A. PA, QA, are produced to meet the dirrecterix in R and T. Then /_RST is equal to

P Q R is a triangle in which P Q=P R and S is any point on the side P Q . Through S , a line is drawn parallel to Q R and intersecting P R at Tdot Prove that P S=P Tdot

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is: