Question

Parabola Help. Write 3y^2+24y+72x-96=0 in standard form. I got (y+4)^2=-24(x-2) is that right? also what is the focus? line of symmetry? Directrix?

Answer 1

you are correct

3y^2+24y+72x-96=0

is equivalent to

(y+4)^2=-24(x-2)

Answer 2

(y+4)^2=-24(x-2)

(y-(-4))^2=-24(x-2)

(y-(-4))^2=-4(6)(x-2)

the equation is now in the form

(y-k)^2 = -4p(x-h)

where in this case

h = 2
k =-4
p = 6

this means that

1) the parabola opens in a horizontal direction, either left or right because of the y^2 term

2) the parabola opens up to the left (since we have a negative -4 on the right side, if it was positive, then it would open up to the right)

3) the value of p determines how far the focus is from the vertex and it determines how far the directrix is from the vertex

4) the focus lies on the axis of symmetry

Answer 3

got it thanks! @jim_thompson5910

Answer 4

tell me what you got for the focus and directrix

Answer 5

oh and forgot to mention that (h,k) is the vertex, but I'm sure you know that already

Answer 6

I got (-4,-4) and 8. vertex:(2,-4) of coarse.

Answer 7

(-4,-4) is the focus, good

x = 8 for the directrix

(2,-4) is the vertex

all 3 are correct

Answer 8

yahoo! (:

Answer 9

lol nice work