SOLUTION: 1. Graph each parabola and clearly indicate the focus, directrix and endpoints at the latus rectum.
y^2 - 8y + 12x - 8 = 0
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Question 1091389: 1. Graph each parabola and clearly indicate the focus, directrix and endpoints at the latus rectum.
y^2 - 8y + 12x - 8 = 0
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The parabola has a y squared term, so it opens right or left. The vertex form for a parabola that opens right or left is
In this form, the vertex is (h,k), the length of the latus rectum is |4p|; and p is the distance from the vertex to the directrix and from the vertex to the focus.
So put the equation for your parabola in that form:
(complete the square in y)
The vertex is (2,4).
4p is -12, so p is -3, indicating that the parabola opens to the left ("in the negative direction").
The directrix is a distance |p| to the right of the vertex; 2+3 = 5, so the directrix is the vertical line x=5.
The focus is a distance |p| to the left of the vertex, at (-1,4).
The length of the latus rectum is 12; since the focus is the midpoint of the latus rectum, the endpoints of the latus rectum are at (-1,10) and (-1,-2).
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