2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
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._., idk u tell me?
To solve the equation of the parabola, I would need to use the distance formula and substitute the focal point in (x1-y1). Also use the distance formula for the directrix. Since it is a straight line, the x part could be eliminated and the remaining part of the formula would be used, substituting the y for the given measurement of the directrix. The two unfinished formulas would be combined and then solve for the equation. f(x) would be the unit of measurement for parabola.
how do I make this directly answer the question better? got it wrong
no clue :/
Please kindly help @jim_thompson5910
"An archway will be constructed over a walkway"
so we know that the parabola opens downward and might look something like this
The focus is always on the inside of the curve with the directrix on the other side of the parabola
if you know where the focal point and directrix are, then you can use them to find the vertex
the vertex is (h,k)
p is the focal distance
you use those bits of info to plug them into 4p(y-k) = (x-h)^2 to get the parabolic equation