I need the formulae to find the endpoints of latus rectum of parabola?

Question

Thanks.

Answer 1

The formula of a vertical parabola in vertex form with vertex (h,k) is:

4p(y - k) = (x - h)²

The axis of symmetry is the vertical line x = h.

The directed distance from the vertex to the focus is p. The focus is therefore (h, k + p).

The latus rectum is perpendicular to the line of symmetry. It runs from one side of the parabola, thru the focus to the other side. Its length is 4p--a distance of 2p in either direction from the focus. The endpoints of the latus rectum are therefore:

(h - 2p, k + p) and (h + 2p, k + p)
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A similar workup could be prepared if the parabola was horizontal.

Answer 2

The general equation of a parabola is y^2=4ax The focus is at the point ( a,0 ). At the focus x=a.....therefore y^2= 4(a^2)....therefore y=2a and y= -2a...coordinates of the ends of the latus rectum are ( a, 2a) and (a,-2a).