Question

Someone help me please oh my god I'm freaking out.
A landscaper wants to plan a walkway that passes between a tree and the border of the lawn. Using these as the focus and directrix, how can the landscaper plan a parabolic path that will be equidistant from the tree and the border at all times? Describe your method in full sentences.

Answer 1

At @ashaboo456, do you have any question in particular about this problem you have posted?

Answer 2

Im confused about pretty much everything, ive been on this question for almost an hour now ugh. Sorry, do you mind helping?

Answer 3

Do you remember that distance formula I gave you for finding the equation of a parabola given the focus and directrix?

Answer 4

Uh, no, sorry omg

Answer 5

If given the focus \((x_1, y_2)\) and directrix \((x_2, y_2)\), you can insert both points into this distance formula:

\((x - x_1)^2 + (y - y_1)^2 = (x - x_2)^2 + (y - y_2)^2\)

Afterwards, you simplify the equation until you have the form:
\(y = a(x - h)^2 + k\) or the form \(x = a(y - h)^2 + k\)

Answer 6

So is that it then? Sorry I feel really stupid right now

Answer 7

because it doesn't give me any points

Answer 8

What I gave you is a general formula. To do this problem, you'll have to make up your own points.

Answer 9

Oh, alright. I think I've got it now. Thank you so much seriously you are a grade saver !