212x
The given equation of parabola is y 2 = 12 x
Here coefficient of x is positive, hence parabola opens in right.
General equation of the parabola is given by y 2 = 4 a x ,(1)
where ( a , 0 ) represents the coordinates of the focus
Given equation y 2 = 12 x can be represented as y 2 = 4 × 3 × x (2)
Compare equation (1) and (2),we find that a = 3 .
Coordinates of focus is given by ( a , 0 ) (3)
Equation of directrix is given by x = − a (4)
Length of latus rectum is given by 4 a (5)
Substitute the value of a in (3), (4) and (5)
Focus= ( 3 , 0 )
Equation of directrix is,
x = − 3 x + 3 = 0
Length of latus rectum = 4 × 3 = 12
Since the given equation involves y 2 the axis of the parabola is the x -axis.
Thus the coordinates of focus is ( 3 , 0 ) ,axis of parabola is x axis, equation of directrix is x + 3 = 0 and length of latus rectum is 12.
The given equation of parabola is
Here coefficient of
General equation of the parabola is given by
where
Given equation
Compare equation (1) and (2),we find that
Coordinates of focus is given by
Equation of directrix is given by
Length of latus rectum is given by 4
Substitute the value of
Focus=
Equation of directrix is,
Length of latus rectum
Since the given equation involves
Thus the coordinates of focus is
