Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x 2 = –9 y
x 2 = − 9 y .
Since coefficient of y is negative, the parabola opens downward.
General equation of the parabola is given by
x 2 = − 4 a y ,(1)
where ( 0 , − a ) represents the coordinates of the focus.
Given equation x 2 = − 9 y can be represented as
x 2 = − 4 × 9 4 × y (2)
By comparing equation (1) and (2),we get a = 9 4 .
Focus= ( 0 , − a ) = ( 0 , − 9 4 )
Equation of directrix is given by y = a
y = 9 4 y − 9 4 = 0
Length of latus rectum = 4 a = 4 × 9 4 = 9
Since the given equation involves x 2 the axis of the parabola is the y -axis.
Therefore, the coordinates of focus are ( 0 , − 9 4 ) ,axis of parabola is y axis, equation of directrix is y − 9 4 = 0 and length of latus rectum is 9.
Since coefficient of
General equation of the parabola is given by
where
Given equation
By comparing equation (1) and (2),we get
Focus=
Equation of directrix is given by
Length of latus rectum =
Since the given equation involves
Therefore, the coordinates of focus are
