22. What is an equation of the parabola with vertex at the origin and focus (-4, 0) ?

a.) x = 1/16y^2

b.) x = - 1/16y^2

c.) y = - 1/16x^2

d.) y = 1/16x^2

The correct answer for the question shown above is the second option (Option b), and the option cwhich is:

b) x = - 1/16y^2

c) y=-1/16x^2

The explanation is shown below:

The focus of a parabola is (h, k+1/4a), then, you have:

h, k = (0,0)

1/4a=1/4 (-1/16)

Then, you obtain:

1/4a=-4

Therefore, the focus of the equation of the parabola x = - 1/16y^2 and the parabola y=-1/16x^2 is F (0-4)

So, as you can see, the correct answer is the options mentioned before, the option b and the option c.