Question

Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7

Answer 1

Answer:

Vertex = (7,5)

Length of latus rectum = 2 units

Step-by-step explanation:

The vertex form of a parabola is

$x=a(y-k)^2+h$    ...(1)

where, (h,k) is vertex and length of latus rectum is $\left|\dfrac{1}{a}\right|$.

The given equation is  

$x=\dfrac{1}{2}(y-5)^2+7$    ...(2)

On comparing (1) and (2), we get

$h=7,k=5,a=\dfrac{1}{2}$

So, vertex of parabola is (7,5).

Length of latus rectum is

$L.R.=\left|\dfrac{1}{a}\right|=\left|\dfrac{1}{\frac{1}{2}}\right|=2$

Therefore, the length of the latus rectum is 2 units.