Question

how do u find the focus, directrix and focus diameter of a parabola with the equation of x^2=y

Answer 1

the general form of equation is x^2=4ay,
then the focus is (0,a) ,
directrix is y=-a

Answer 2

the general from of a parabola is x^2 = (4a)y ; where a is the distance from the vertex to the foci in one direction; and the distance between the vertex and the directix in the other direction

Answer 3

x^2 = y has no extra numbers to shift it around; so we say it is centered at the origin; with a vertex of (0,0)

Answer 4

x^2 is always a positive number; so the parabola opens upwards

Answer 5

k, but if i am trying to graph it the focus would be (0,1) ?

Answer 6

4ay = y ; /y

4a = 1 ; /4

a = 1/4

Answer 7

x^2=4(1/4)*y
so the coordinates of the focus is (0,1/4) and y=-1/4 is the equation of directrix...

Answer 8

its ust confusing because i dont have the a and y in the original equation

Answer 9

it best to commit the general equation to memory if you are wanting to pursue a career in the maths.

x^2 = 4ay; is the general

x^2 = y; is the given

which means that 4ay = y and then solve for 'a'

Answer 10

k im following ya

Answer 11

that is the process I posted above; since 'a' is the determing part of the question

Answer 12

4ay = y ; divide out the y

4a = 1 ; divide out the 4

a = 1/4 ; and this is the distance from the vertex to the foci; and the distance from vertex to the directix

Answer 13

the foci is in the direction of the upward curve; and the directix sits behind the vertex

Answer 14

vertex = (0,0) ; and graph opens up; so the y component increases by |a|

foci = (0,1/4)

directix is the other side of it; y = 0-1/4; y=-1/4