Answer:
The Focal length of the parabola is [tex]p=\frac{2}{3}[/tex]
Step-by-step explanation:
Given : Parabola equation [tex]y-4=\frac{3}{8}x^2[/tex]
To find : What is the focal length of the parabola with the equation?
Solution :
The given parabolic equation is
[tex]y-4=\frac{3}{8}x^2[/tex]
The general form of the parabola is [tex](y-k)=\frac{1}{4p}(x-h)^2[/tex]
Where, (h,k) are the vertex of the parabola and p is the focal length.
On comparing with [tex]y-4=\frac{3}{8}x^2[/tex]
(h,k)=(0,4) is the vertex of the parabola
The focal length is
[tex]\frac{1}{4p}=\frac{3}{8}[/tex]
[tex]p=\frac{8}{3\times 4}[/tex]
[tex]p=\frac{2}{3}[/tex]
So, The Focal length of the parabola is [tex]p=\frac{2}{3}[/tex]
