AB is a chord the parabola `y^(2)=4ax` with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The projection 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

PQ is a chord ofthe parabola y^2=4x whose perpendicular bisector meets the axis at M and the ordinate of the midpoint PQ meets the axis at N. Then the length MN is equal to

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 tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

A square has one vertex at the vertex of the parabola y^2=4a x and the diagonal through the vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the coordinates of the vertices of the square are (a) (4a ,4a) (b) (4a ,-4a) (c) (0,0) (d) (8a ,0)

The axis of the parabola (y +1)^(2)=- 4(x - 3) is parallel to_

A chord overline(PQ) of the parabola y^(2) =4ax , subtends a right angle at the vertex , show that the mid point of overline(PQ) lies on the parabola, y^(2) = 2a (x - 4a) .

Length of the shortest normal chord of the parabola y^2=4ax is

L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A passing through a point O on its axis. Prove that the radical axis of the circles described on L L ' and M M ' as diameters passes though the vertex of the parabola.