What are the focus and directrix of the parabola with the given equation x = -1/8y²

Solution:

Given equation is x = -1/8y²

⇒ y² = -8x ---(1)

Equation (1) represents the standard form of parabola y² = 4ax.

Comparing equation (1) with the standard form we get, 

4a = -8 

∴ a = -2

Focus = (a, 0) = (-2, 0)

Directrix : x = -a

⇒ x = -(-2) = 2

What are the focus and directrix of the parabola with the given equation x = -1/8y²

Summary:

The focus and directrix of the parabola with the given equation x = -1/8y² are a = -2 and x = 2.