Concept explainers
(a)
To define:
The geometric definition of a parabola.
Answer to Problem 1CC
A parabola is a set of points in the plane such that every point is at equal distance from the fixed point and fixed line.
Explanation of Solution
Given information:
The curve is parabola.
Calculation:
Consider any equation of curve as
The graph of the equation
The
This
The every point on the curve of the graph is equidistance to the fixed point called as focus and fixed line called as directrix..
Therefore, the parabola is a set of points in the plane that every point is at equal distance from the fixed point and fixed line
Conclusion:
Thus,a parabola is a set of points in the plane that every point is at equal distance from the fixed point and fixed line.
(b)
To find:
The equation of parabola with vertex at the origin and with vertical axis, also find focus and directrix.
Answer to Problem 1CC
The equation of parabola is
Explanation of Solution
Given information:
The parabola passes through the origin.
Calculation:
The parabola passes through the origin and the vertex of the parabola is
Consider a focus of the parabola as
The equation of parabola can be obtained as
Conclusion:
Thus, the equation of parabola is
(c)
To sketch:
The graph of the equation
Explanation of Solution
Given information:
The equation of parabola is
Concept used:
If the equation of parabola is
Graph:
The given equation can be written as
Compare the given equation
Therefore, the focus of the parabola is
The graph of the equation of parabola is shown in Figure 1.
Interpretation:
From Figure 1, it is observed that the focus of the parabola is
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Chapter 7 Solutions
College Algebra
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