Concept explainers
- (a) Give the geometric definition of a parabola.
- (b) Give the equation of a parabola with vertex at the origin and with vertical axis. Where is the focus? What is the directrix?
- (c) Graph the equation x2 = 8y. Indicate the focus on the graph.
(a)
To state: The geometric definition of parabola.
Explanation of Solution
The geometric definition of parabola is stated as follows,
The set of points on a plane which are equidistance from a fixed point and a fixed line is called a parabola. Where the fixed point is called the focus and the fixed line is called the directrix.
(b)
To give: The equation of parabola with vertex at the origin and with vertical axis and find the focus and the directrix.
Answer to Problem 1RCC
The equation of the parabola with vertex at the origin and with vertical axis is
When
When
When
When
Explanation of Solution
Definition used:
“The equation of the parabola with vertex
By the definition stated above the parabola
In case of
In case of
(c)
To graph: The parabola
Answer to Problem 1RCC
The focus and directrix of the parabola
The graph of the parabola
From Figure 1, it is observed that the focus is at
Explanation of Solution
Compare the equation
Therefore, by the definition stated above, focus is
Thus, the focus and directrix of the parabola
The graph of the parabola
From the Figure 1, it is observed that the focus is at
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Chapter 11 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
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