answer the questions in this part of the task based on your understanding of the definition and the standard equation for the conic you chose.
part a and b if you can
a. inspect the equation for the type of conic section you chose. what attributes are necessary to graph it? be sure to include specific points or equations to complete your answer.
b. explain how, if you have the attributes given below for the conic you chose, you can derive its equation in standard form (see the attachment)

Attached

Step-by-step explanation:

Choosing the parabola

(x-2)²=12(y-2)

The attributes necessary to graph it are the vertex and focus

If you have the attributes above, you can derive the equation in standard form as

The standard equation of a parabola is

(x-h)²=4p(y-k)

compare with your equation

(x-h)²=4p(y-k)

(x-3)²=12(y-2).......................here you can find value of p

4p=12...............divide by 4 both sides

p=12/4=3

Vertex is at (h,k) = (3,2)

The focus is at (h+p,k)

but p=3 hence

focus is (3+3,2) = (6,2)

Using focus point (6,2) and the vertex point (3,2) you can derive the equation of the parabola as

(x-h)²=4p(y-k)

(x-3)²=4(3)(y-2)

x²-6x+9=12(y-2)

x²-6x+9=12y-24

x²-6x-12y+9+24=0

x²-6x-12y+33=0

see attached

d) 48

step-by-step explanation:

16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,304,320,336