#1**+1 **

Q1

We have the form

( y - k)^2 = 4a ( x - h)

The vertex is given by ( h, k) = (3, -1)

Since y is squared and we have no negatives on either side of the equation, it opens to the right

4a = 12

a = 3 which means that the focus is 3 units to the right of the vertex

The directrix is 2a = 2(3) = 6 units from the focus

The focus is at ( 3 + 3, -1) = (6 - 1)

The dirctrix has the equation x = (x coordinate of the vertex - a) = (3 - 3) = 0

So x = 0

Here's the graph : https://www.desmos.com/calculator/jrejmuykh9

CPhill Nov 19, 2019

#2**+1 **

Q2

The directrix is to the left of the focus...so....this parabola opens to the right....therefore...we will hav no negatives on either side of the equation

The form will be

(y - k)^2 = 4a (x - h)

The vertex is given by ( (sum of directrix + x coordinate of the focus ) / 2, y coordinate of focus ) =

( [ 0 + 2]/2 , 6) = (1, 6) = (h, k)

"a" is the distance from the vertex to the focus = 1

So we have

(y - 6)^2 = 4(1) ( x - 1)

( y - 6)^2 = 4 ( x - 1)

Here's the graph : https://www.desmos.com/calculator/1y3feymzzs

CPhill Nov 19, 2019