1. the equation of a parabola is given. y = 1/8x^2 + 4x + 20 what are the coordinates of the focus of the parabola? 2. the equation of a parabola is (y - 1)^2 = 16(x + 3). what is the equation of the directrix of the parabola?

Question 1)

The given parabola is:



First we need to convert this equation to the general form similar to:



So, the given equation will be:



Comparing given equation with the general equation, we can write:
p = 2
h = -12
k= -16

The focus of the parabola with squared x terms lies at (h , k+p)
Using the values, we get the focus point of the given parabola (-16, -10)

Question 2.

The equation of the parabola is:


This means:
p=4
h = -3
k =1

The directrix of the parabola with squared y term has the equation of the form:

x = h - p

Using the values, we get

x= - 3 - 4 = -7

So, the equation of the directrix of the parabola will be x = -7