Question

If they stake the pony where David wants, what is the equation of the circle that represents the pony’s path?

Answer 1

Is this question implying that the pony is attached to a rope and is tied to a stake?

Answer 2

yes

Answer 3

Please give us more information if we are going to help you out with this question. This post is unsolvable with limited information if you want us to help please inform us more.

Answer 4

This information requires us to download the (PDF), could you give us any other info on this question?

Answer 5

please the rainbow text is killing my eyes xD

Answer 6

You could take a picture of it and send it through the (Attach Files) button.

Answer 7

Like maybe say (Somthing on a page/paper)?

Answer 8

Thank you.

Answer 9

ofc

Answer 10

The point is at (16, 18)

Answer 11

so hes putting it at the same point as the rose bush?

Answer 12

The question is just super confusing to me

Answer 13

who me? Cuz nah tbh

Answer 14

@smokeybrown

Answer 15

The document you posted says that David wants to "put the rope 10 feet up and 10 feet over". It's not very clearly written, but I think this means that the stake where the rope starts would be 10 feet up and over relative to the origin. I guess this means David wants to put the stake at the coordinate point (10, 10)

I think the question should have specified in what direction (left or right) "over" to put the rope, and relative to what (the origin? the rose bush?) But given the context, that's my interpretation

And by the same reasoning, it sounds like Joel's plan is to put the stake at (8, 8)

Answer 16

yea ok that makes sense

Answer 17

Great! So with that, we should have all the information we need to find the equation of the circle for each of the plans.

Recall that the equation of a circle is
\[(x-a)^2 +(y-b)^2 = r^2\]
where (a, b) is the center of the circle, r is the radius, and (x, y) can be any point along the edge of the circle
We know (a, b) , which is the point where the stake is set. And the radius is given as the length of the rope, 10

Answer 18

(x-10)^2+(y-10)^2=10^2*

Answer 19

You fixed the typo :)
Yep, that's right, you got the equation for the circle according to David's plan

Answer 20

okay thank yu sm who eva u are.

Answer 21

So now i do the same thing for Joys plan?

Answer 22

Right, you can follow the same process if you want to find the equation for the circle in Joey's plan too

Answer 23

how would i do this ?To check whether the rose bush lies on the circle, see if its coordinates make the equation for the circle true. Show your work.

Answer 24

for joys plan

Answer 25

You need to show your own work if @smokeybrown does end up showing his work for how he did it then you are not allowed to copy paste your answer as his.

Unless this is another question? For which if it is then, please give us more (information) ℹ️ on it please so we are able to explain this question to you in a formal direct way.

Answer 26

Oh and also put it in another post, thank you 🙏

Answer 27

If question 10 is about David's plan, we can use the equation you found earlier for the equation of the circle by David's plan, (x-10)^2+(y-10)^2=10^2
We can plug in the x and y values of the rose bush's coordinates (16, 18) to the equation, and see if the equation is true
(16-10)^2+(18-10)^2=10^2
(6)^2 + (8)^2 = 100
36 + 64 = 100
100 = 100
So, it looks like the equation is true, which means the rose bush falls along the edge of the circle

Answer 28

Thank you. But this is about Joys plan (8,8)

Answer 29

I see. In that case, we can use the equation for Joy's plan and follow the same process:
(16-8)^2+(18-8)^2=10^2
(8)^2 + (10)^2 = 100
64 + 100 = 100
164 = 100
This is not true, which means that the location of the rose bush is not along the circle. Think of the left side of the equation "164" as representing the distance of the rose bush from the stake; the right side "100" represents the distance that the rope can extend from the stake. The rose bush is farther than the rope can extend, which means the rose bush is located outside of the circle

Answer 30

Okay. So then for 11 is the pony able to move around freely without running into the fence?