SOLUTION: What would be the length of latus rectum and vertex of the parabola 3x=y2

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Question 1040915: What would be the length of latus rectum and vertex of the parabola 3x=y2
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
3%28x-h%29=%28y-k%29%5E2
3%28x-0%29=%28y-0%29%5E2
Vertex is (0,0), the Origin.


Compare 3%28x-0%29=%28y-0%29%5E2 to 4p%28x-0%29=%28y-0%29%5E2.
p is the distance from vertex to either focus or directrix. Your parabola is horizontal and the vertex is on the left for minimum x value, and focus is to the right of the vertex.
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4p=3
p=3%2F4
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The focus is at ( 3/4, 0).


Endpoints of Latus Rectum:
y%5E2=3x
y=0%2B-+sqrt%283x%29
y=0%2B-+sqrt%283%283%2F4%29%29
y=0%2B-+3%2F2

The focus is ON the x-axis;
Latus Rectum is from the upper y-value to the lower y-value at the focus.
%283%2F2%29%2A2
highlight%28LatusRectumLength=3%29


Study your book's lesson on this and related, and also study derive equation for parabola of given focus and directrix and same thing, different orientation, but vertex NOT at Origin