The distance between the focus and the directrix.
It has been determined that the distance between the focus and the directrix of the given parabola is
Given:
The vertex of a parabola is
Concept used:
Each point on a parabola (including the vertex) is equidistant from a point called the focus and a line called the directrix.
Calculation:
As discussed, each point on a parabola (including the vertex) is equidistant from the focus and the directrix.
Then, the vertex is equidistant from the focus and the directrix.
According to construction of a parabola, the vertex lies on the line segment drawn from the focus, perpendicular to the directrix.
This implies that the distance between the focus and the directrix is the sum of the distance between the vertex and the focus and the distance between the vertex and the directrix.
Since the vertex is equidistant from the focus and the directrix, the distance between the vertex and the directrix equals the distance between the vertex and the focus.
Hence, the distance between the focus and the directrix is twice the distance between the vertex and the focus.
It is given that the vertex of a parabola is
Then, the distance between the focus and the directrix is
Conclusion:
It has been determined that the distance between the focus and the directrix of the given parabola is
Chapter 10 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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