Question

3. y2--8x

Answer 1

The given equation of parabola is y 2 =−8x

Here coefficient of x is negative, hence parabola opens in left.

General equation of the parabola is given by y 2 =−4ax ,(1)

where ( −a,0 ) represents the coordinates of the focus

Given equation y 2 =−8x can be represented as y 2 =−4×2×x (2)

Compare equation (1) and (2),we find that a=2 .

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= (−2,0)

Equation of directrix is,

x=( −( −2 ) ) x=2 x−2=0

Length of latus rectum =4×2 =8

Since the given equation involves y 2 the axis of the parabola is the x -axis.

Thus the coordinates of focus is ( −2,0 ) ,axis of parabola is x axis, equation of directrix is x−2=0 and length of latus rectum is 8.