Question

A parabola has directrix y=-3, axis x=4 and latus rectum equal to 2. Find its equation.
pls help :)

Answer 1

i can yes ... do you recall what a latus rectum is?

Answer 2

uhmm. its a chord that passes through the focus? hahaha.. im not that sure though. :D

Answer 3

youre right actually :) i have an idea on how to do this

Answer 4

lets create a parabola that fits, then move it into place

Answer 5

ok. :)

Answer 6

this distance between focus and directrix should be 6 ... so lets have a parabola of vertex 0,-3 with roots of -1,0 and 1,0 this gives us a width of 2 at the focus

Answer 7

so....

f(x) = a(-1-x)(1-x), such that f(0) = -3

-3 = a(-1)(1), a=3

our parabola to move is therefore

f(x) = 3(-1-x)(1-x) , but how to move it?

Answer 8

we need to raise it by 3, and move it to the right by 4

Answer 9

so the alterations are:

f(x) = 3(-1-(x-4))(1-(x-4)) + 3

and from that we can simplify it to our hearts content

Answer 10

ohh because of axis x=4?

Answer 11

yes, and i have to review my setup since i evidently got something off along the way