Question

I already found the vertex, but can someone help me find the latus rectum of this parabola?

Answer 1

Explanation:

y=x²+7

vertex(0,7)

the length of latus rectum in a parabola equal to four times the focal length :

y=x²+7

focus X=-b/2a=0

focus Y=c- (b²-1)/4a=7+1/4=29/4

focus (0 , 29/4)

latus rectum is 29/4

(x-h)^2 = 4p (y-k) 4p is the length of the latus rectum with vertex(0,7)

(0-0)²=4p(29/4-7)

0=29p-28p=1p

the length of the latus rectum is 1

Answer 2

1

Explanation:

The short answer is that the length of the latus rectum is the reciprocal of the magnitude of the leading coefficient.

In y = x^2 +7, the leading coefficient is 1.

latus rectum = 1/|1| = 1