If the equation of the parabola is y² = -8x. Then the focus is at (-2, 0) and the directrix is at x = 2.
What is the parabola?
It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.
The equation of the parabola is given below.
[tex]\rm x=-\dfrac{1}{8} \times y^2[/tex]
On simplifying, we have
[tex]\rm y^2 = -8x\\\\y^2 = -4(2)x[/tex] ...1
We know that equation of the parabola
[tex]\rm y^2 = -4ax[/tex] ...2
Then the directrix is at x = a and the focus will be (-a, 0)
Compare equations 1 and 2, we have
a = 2
Then the focus is at (-2, 0) and the directrix is at x = 2.
More about the parabola link is given below.
https://brainly.com/question/8495504
