Question

Find the focal width. Can you please help with this? Thanks

Answer 1

Notice that the graph of the function is a parabola that opens downwards.

In general, a parabola that opens upwards/downwards is given by the expression below

`\begin{gathered} (x-h)^2=4p(y-k) \\ p\rightarrow focal\text{ distance} \end{gathered}`

Thus, in our case,

`\begin{gathered} -(1)/(20)x^2=y \\ \Rightarrow x^2=-20y \\ \end{gathered}`

After comparing the former result with the equation above,

`\begin{gathered} \Rightarrow4p=-20 \\ \Rightarrow p=-5 \end{gathered}`

And the focal width is equal to |4p|; therefore,

`\begin{gathered} \Rightarrow focal\text{ width}=|4p|=|4*-5|=|-20|=20 \\ \end{gathered}`

Therefore, the answer is focal width=20 units