Answer:
Vertex = (7,5)
Length of latus rectum = 2 units
Step-by-step explanation:
The vertex form of a parabola is
[tex]x=a(y-k)^2+h[/tex] ...(1)
where, (h,k) is vertex and length of latus rectum is [tex]\left|\dfrac{1}{a}\right|[/tex].
The given equation is
[tex]x=\dfrac{1}{2}(y-5)^2+7[/tex] ...(2)
On comparing (1) and (2), we get
[tex]h=7,k=5,a=\dfrac{1}{2}[/tex]
So, vertex of parabola is (7,5).
Length of latus rectum is
[tex]L.R.=\left|\dfrac{1}{a}\right|=\left|\dfrac{1}{\frac{1}{2}}\right|=2[/tex]
Therefore, the length of the latus rectum is 2 units.
