Question

a vertical parabola has vertex at (-3,-2) and passes through the point (-1,7). Find the equation of the parabola, the equation of the directrix, and the coordinates of the focus point. Please explain!!

Answer 1

let's get the vertex form first and then work the others from there...

so the vertex is at (-3, -2) and the parabola passes through the point (-1, 7).

we can use this to get the vertex form of the parabola first...
\[y=f(x)=a(x-h)^2+k\]this is the vertex form with vertex at (h, k). sub in those know values. what do you get?

Answer 2

y=a(x+3)^2-2

Answer 3

good. now use the given point to find what a is.

Answer 4

9/4

Answer 5

is that correct

Answer 6

yeppers!

so know to translate to the directrix thingymabobber...

\[4p(y-k)=(x-h)^2\]
has distance p to the focus or directrix from the vertex (h, k)

Answer 7

you just found\[y=\frac{5}{4}(x+3)^2-2\]now work it into the form above and find p.

Answer 8

you mean 9/4?

Answer 9

yeah, sorry

Answer 10

p= 1/9? which is the directrix?

Answer 11

p = 1/9 but i't not the directrix... it's the distance from the vertex to the focus and it's the distance from the vertex to the directrix.

Answer 12

so how does that help me find the focus and the directrix

Answer 13

directrix is gonna be like this...

y = k - p

focus is at the point (h, k + p)

Answer 14

Thannkss sooo muchhh!!!! do you know multidimensional calculus?

Answer 15

it's been a while... whatcha got?

Answer 16

im taking the class and we just calculated the volume of an ellipse using line integrals derived from double integrals. if I wanted to calculate the volume of an ellipsoid, how would do that?

Answer 17

you'd be better off asking someone more familiar than me. i could do it but it would be long and arduous.

Answer 18

okay thanks!! I have one more question.. will u be on later