To show: why the pencil traces a parabola.
Answer to Problem 46E
The pencil traces a parabola because the length of the string is unchanged.
Explanation of Solution
Given:
Calculation:
This happens because the length of the string is unchanged. This is so because the string is inextensible.
Here,
Assume at the beginning,
Now, as the T square comes closer to the focus point
Now the distance between the point
And correspondingly, the string length would reduce to
According to our assumption,
This is nothing but the locus of a parabola (locus of a point that moves such that the distance of the point from a fixed point is equal to its distance from a fixed line).
Conclusion:
Therefore, the pencil traces a parabola because the length of the string is unchanged.
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
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