Given:
There is a diagram given in the question
Required:
We need to find the equation of parabola and focus
Explanation:
As we can see that vertex point of parabola is origin
[tex](0,0)=(h,k)[/tex]
the general equation of parabola is
[tex]y=a(x-h)^2+k[/tex]
now substitute the values
[tex]y=ax^2[/tex]
now by diagram there is a point
[tex](60,20)[/tex]
we use this point to find the a
Plug the point in equation
[tex]\begin{gathered} 20=a(60)^2 \\ \frac{20}{3600}=a \\ \\ a=\frac{1}{180} \end{gathered}[/tex]
Now the equation of parbola is
[tex]y=\frac{x^2}{180}[/tex]
now the coordinate of focus is
[tex](h,k+\frac{1}{4a})[/tex]
substitute all the values
[tex]\begin{gathered} (0,0+\frac{1}{\frac{4}{180}}_) \\ \\ (0,45) \end{gathered}[/tex]
Final answer:
Coordinate of focus is
[tex][/tex]
