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option:AVertex: (0,0)Focus: (0,-4)Directrix: y=4focal width: 16Step-by-step explanation:Part 1:we are given a equation of a parabola as:on converting the equation of parabola into the standard form of: we have vertex as (h,k).so here the equation is converted as:we have h=0,k=0 and p= -4so, we have vertex as (0,0).now the focus is given as (h,k+p)hence focus is:(0,-4)directrix is given by the formula y=k-pHence, directrix is:y=4.focal width of a parabola is given by |4 p|Hence, Focal width is: 16.Hence,...

Pl if you are stalker don t even think to answer

Ответ:

Gtx014

16.03.2023

Mathematics

option:A

Vertex: (0,0)

Focus: (0,-4)

Directrix: y=4

focal width: 16

Step-by-step explanation:

Part 1:

we are given a equation of a parabola as:

$y= \frac{-1}{16}\times x^2$

on converting the equation of parabola into the standard form of:

4p(y-k)=(x-h)^2 we have vertex as (h,k).

so here the equation is converted as:

4(-4)(y-0)=(x-0)^2

we have h=0,k=0 and p= -4

so, we have vertex as (0,0).

now the focus is given as (h,k+p)

hence focus is:(0,-4)

directrix is given by the formula y=k-p

Hence, directrix is:y=4.

focal width of a parabola is given by |4 p|

Hence, Focal width is: 16.

Hence, option A is correct.

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