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

Question

asked Mar 23, 2021 137k views

1 Answer

Buboh · Answer 1 · 2021-03-27T12:15:12+0000

Answer:

Vertex = (7,5)

Length of latus rectum = 2 units

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
$\left|(1)/(a)\right|$ .

The given equation is

x=(1)/(2)(y-5)^2+7 ...(2)

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

h=7,k=5,a=(1)/(2)

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

Length of latus rectum is

$L.R.=\left|(1)/(a)\right|=\left|(1)/((1)/(2))\right|=2$

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