Question

Graph the equation. Identify the vertex, axis of symmetry, focus and directrix of the prabola.

x^2=8y

Answer 1

@mathstudent55 @mathslover @mathmale

Answer 2

Put to use the knowledge you gained from this last problem. Does this parabola open up, down, left or right? Why?

Answer 3

up

Answer 4

x^2

Answer 5

Great! that's correct.

Now, one of the standard equations of a vertical parabola that opens UP is

4py=x^2. Have you seen this before? If so, what does that "p" stand for?

Answer 6

focus?

Answer 7

"focus" certainly is part of the picture. Try finishing this statement: "p represents the distance between the ( ? ) and the ( ? ) in the graph of a parabola whose vertex is at (0,0)."

Answer 8

distnace and midpoint idk...

Answer 9

p is the distance between the focus and the vertex.

The parabola in question is a vertical one.

Therefore, the distance between the focus and vertex is measured (horizontally, vertically) (which one?)

Answer 10

vertivally

Answer 11

Very good.

So, again,

4py=x^2 may be compared with y our
8y = x^2. What is the value of p in this case?

Answer 12

Hint: 4py = 8y.

Solve for p.

Answer 13

2

Answer 14

Good. You may or may not know that if you have a parabola with equation 4py=x^2, the vertex is at (0,0). You correctly determined that the value of p is 2. Please put these facts to use by determining the location of the focus. Starting at the origin (the vertex), should you go up, down, left or right, to arrive at the focus?

Answer 15

up i get it thanks do u happen to know the equaition of a circle?

Answer 16

Write the equation tof the circle that passes through the given point and whose center is the origin.
(-2,-4)

Answer 17

I strongly urge you to look up "equation of a circle" on the Internet yourself if you need to know / learn it. Just this one time I have done that search for you:

https://www.google.com/search?q=alternate+exterior+angles&rlz=1C1CHFX_enUS461US461&oq=alternate+exterior+angles&aqs=chrome..69i57j0l5.5575j0j7&sourceid=chrome&espv=210&es_sm=122&ie=UTF-8#q=equation+of+a+circle

The equation of a circle with center at (0,0) is simpler than the equation for a circle centered at (h,k).

If at (0,0), the equation is x^2 + y^2 = ??? (you finish this, please.)

Answer 18

It's your job to find that ??? in my previous post.

When you have that value,

Write the equation of this particular circle as x^2 + y^2 = ???