Question

Find the focus ,equation of directrix and length of latus rectum of the parabola y2=8x​

Answer 1

Step-by-step explanation:

Equation of the parabola y

2

=−4ax

Since the coefficient of x is negative the curve is open towards left.

Coordinates of focus is (-a, 0)

Length of the latus rectum is 4a.

Equation of directrix is x-a = 0

The given equation is y

2

=−8x

Comparing this equation with y

2

=−4ax

4a=8

a=2

Hence the coordinates of focus are (-2,0)

Since the given equation involves y

2

, the axis of the parabola is x-axis.

Axis : x-axis

Equation of the directrix : x=a i.e.x=2

Length of the latus rectum :4a=4×2=8