Concept explainers
(a)
To graph: The circle
(a)
Explanation of Solution
Given information:
The equation of circle is
Graph:
The equation
Hence, the points on the circle are
Now consider the parabola
The points on the parabola
The graph of a circle
Interpretation:
The graph represents the parabola
(b)
The solution of the system of equations
(b)
Answer to Problem 2CR
Solution:
The solutions of system of equations
Explanation of Solution
Given information:
The given system of equations is:
Formula used:
For a
Calculation:
Consider the system of equations,
Multiply equation (1) by
Add equations(2) and (3),
Here,
Substituting these values in the quadratic formula,
Substituting these values of
These two solutions are undefined since
Therefore, the system has solutions
Hence, the solutions are
(c)
The points of intersection for circle
(c)
Answer to Problem 2CR
Solution:
The points of intersection for circle
Explanation of Solution
Given information:
The equation of circle is
Formula used:
For a quadratic equation of the form
Calculation:
From part (b),
The solutions of the system of equations
Therefore, the graphs of circle and parabola intersect at these points.
Hence, the point of intersection of circle and parabola are
Chapter 12 Solutions
Precalculus
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