`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`

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.

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at R . Prove that: (i) A R=2B C (ii) B R=2\ B Q

If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A parallel to C P meets C B produced in Q and the parallelogram P B Q R completed. Show that a r(^(gm)A B C D)=a r(^(gm)B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(^(gm)A B C D)=a r(^(gm)B P R Q)

P is the mid-point of side A B of a parallelogram A B C D . A Line through B parallel to P D meets D C at Q and A D produced at R . Prove that (i) A R=2B C (ii) B R=2B Qdot

A B C D is a quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in figure. Prove that a r (triangle A B P) =a r (Quad. A B C D) .

The side A B of a parallelogram A B C D is produced to any point Pdot A line through A parallel to C P meets C B produced in Q and the parallelogram P B Q R completed. Show that a r(llgm A B C D)=a r(llgm B P R Q)dot CONSTRUCTION : Join A C and PQ. TO PROVE : a r(llgm A B C D)=a r(llgm B P R Q)

P Q R is a triangle is which P Q=P R\ a n d\ 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 T

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