a y . Therefore y Hence y = ± The end points of latus rectum are ( , and ( , - Therefore length of the latus rectum LL ′ = . Note The standard form of the parabola y ax has for its vertex( , ) , axis as x -axis, focus as ( , ) a . The parabola y ax lies completely on the non-negative side of the x- axis.
Replacing y by – y in y = ax, the equation remains the same. so the parabola y ax is symmetric about x -axis; that is, x -axis is the axis and symmetry of y ax (ii) Parabolas with vertex at ( , ) h k When the vertex is ( , ) h k and the axis of symmetry is parallel to x -axis, the equation of the parabola is either ( a x h or ( a x h (Fig. . , .
). When the vertex is ( , ) h k and the axis of symmetry is parallel to y -axis, the equation of the parabola is either ( h a y or ( h a y (Fig. . , .
). - - Two Dimensional Analytical Geometry - II Equation Graph Vertices Focus Axis of symmetry Equation of directrix Length of latus rectum a x h (a) The graph of a x h Fig. . ( , ) h k h h a a x h (b) The graph of a x h Fig.
. ( , ) h k h h a h a y (c) The graph of h a y Fig. . ( , ) h k + h a h a h a y (d) The graph of h a y Fig.
. ( , ) h k + −+ h k x h a S ( h + a,k ) A ( h,k ) x = h – a x' y' Directrix S ( h – a,k ) A ( h,k )