Question

Find the vertex, focus, directrix, and focal width of the parabola. negative 1 divided by 12 times x squared = y

Answer 1

negative 1 divided by 12 times x squared = y

`(-1)/(12) x^2=y`

To find vertex we use formula x= -b/2a

From the given equation a= -1/12 and b =0

Plug in the values in the formula

`x= (0)/((-1)/(12)) =0`

Now plug in x=0 in the given equation and find out y

`(-1)/(12)(0)^2=y`

So y=0

Hence vertex is (0,0), h=0 and k =0

Focus is (h, k+p)

We need to find out p

We know a= -1/12

p = 1/4a

`p = (1)/(4(-1)/(12)) = -3`

So focus is (0,0-3) that is (0, -3)

Directrix is y = k - p

We know p = -3 and k=0

y = 0 -(-3) = 3. so directrix is y = 3

Focal width = |4p|

We know p = -3

so it becomes |4(-3)| = 12

Focal width = 12