Mathematics, 17.07.2021 08:40 weeblordd
Where does the 4p come from in (x-a)^2 = 4p(y-k) when dealing with the focus and directrix of a parabola.
Going to use (a, b) as the focus and y = k for the directrix
Mostly going to be talking about vertical parabolas, but I think I can use whatever answers I get to figure out horizontal ones. Everything I'm writing out here I've figured out for both.
Equating the distance between the focus and a point on the graph (namely the vertex) and the vertex and directrix gets me
Then expanding and rearranging I get Whichh I rearrange to because it's in y=f(x) form and it's basically a complicated vertex form.
Using that information and assuming I have a simple vertex form of a parabola and want to find the focus and directrix, where my Parabola is in the form A(x-C) + D and 2D = b + k, which is enough to find the focus and directrix since the x coordinate of the focus will be a in or C in A(x-C)^2 + D (for vertical parabolas anyway)
I've seen the whole (x-a)^2 = 4p(y-k) form though and I'm wondering where that is from, and how it is derived. According to it the focus would be (h, k+p) and the directrix would be y = k-p. Totally expecting it to be simple and something I'm just missing lol
Answers: 3
Mathematics, 21.06.2019 20:00
Someone answer asap for ! max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a. the median of max’s data is 250 b. more than half of the data points max recorded were 177 centimeters. c. a data point chosen at random is as likely to be above the mean as it is to be below the mean. d. every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.
Answers: 1
Mathematics, 22.06.2019 02:00
Mariano delivers newspaper. he always puts 3/4 of his weekly earnings in his savings account and then divides the rest equally into 3 piggy banks for spending at the snack shop, the arcade and the subway
Answers: 2
Where does the 4p come from in (x-a)^2 = 4p(y-k) when dealing with the focus and directrix of a para...
History, 25.03.2020 05:15
English, 25.03.2020 05:15
History, 25.03.2020 05:16
Mathematics, 25.03.2020 05:16
Computers and Technology, 25.03.2020 05:16
Mathematics, 25.03.2020 05:16
Mathematics, 25.03.2020 05:17
History, 25.03.2020 05:17