Concept explainers
To find: The number of points that passes in parabola
Answer to Problem 32E
There would be infinite number of parabolas passing through the two points.
Explanation of Solution
Given information:
To draw the parabola through the two points with different x-coordinates.
Formula used:
Calculation:
Equation of a parabola is
A parabola passing through 2 points give two linear equations with three variables that need to be satisfied.
Let
This gives
Consider two cases:
Case 1:
Solution would be
Case 2: Let none of the abscissa is zero:
Note that slope of the lines are not same as different m-coordinates are given. Considering c as given, we know that solution of a and b exists as function of c if the slope of the lines are not same.
As a result, we have infinite solutions of the system of linear equations.
Thus, there would be infinite number of parabolas passing through the two points.
Conclusion:
There would be infinite number of parabolas passing through the two points.
Chapter 8 Solutions
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