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2 answers:
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Answer:
The endpoints of the latus rectum are and
.
Step-by-step explanation:
A parabola with vertex at point and whose axis of symmetry is parallel to the y-axis is defined by the following formula:
(1)
Where:
- Independent variable.
- Dependent variable.
- Distance from vertex to the focus.
,
- Coordinates of the vertex.
The coordinates of the focus are represented by:
(2)
The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that ,
and
, then the latus rectum is between the following endpoints:
By (2):
By (1):
There are two solutions:
Hence, the endpoints of the latus rectum are and
.