The focus of parabola is (1,5) and its directrix is x + y + 2 = 0. Find the equation of the parabola, its vertex and length of latus rectum.
let F (1,5) be the focus of the parabola and the equation of the directrix is ...........(1)
let P(h.k) be any point on the parabola.
the distance from the focus to the point P = the distance from the directrix to the point P
put h = x and k = y
is the required equation of the parabola.
the axis of parabola passes through the focus and perpendicular to the directrix.
the slope of axis = [since slope of directrix is -1]
the equation of axis is
the point of intersection of axis and directrix is intersection point of eq(1) and eq(2)
the coordinates of k are (-3,1).
vertex is the mid-point of focus and point K
i.e. coordinates of vertex are
now distance from vertex to focus =
the length of the latusrectum =
hope this helps you
let P(h.k) be any point on the parabola.
the distance from the focus to the point P = the distance from the directrix to the point P
put h = x and k = y
is the required equation of the parabola.
the axis of parabola passes through the focus and perpendicular to the directrix.
the slope of axis = [since slope of directrix is -1]
the equation of axis is
the point of intersection of axis and directrix is intersection point of eq(1) and eq(2)
the coordinates of k are (-3,1).
vertex is the mid-point of focus and point K
i.e. coordinates of vertex are
now distance from vertex to focus =
the length of the latusrectum =
hope this helps you