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

Question

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

0

Answers ( No )

    0
    2021-10-11T04:53:45+00:00

    negative 1 divided by 12 times x squared = y

    \frac{-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= \frac{0}{\frac{-1}{12}} =0

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

    \frac{-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 = \frac{1}{4\frac{-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

Leave an answer

Browse
Browse