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Find the angle of intersection between the pair of curves:
Solution:
To illustrate the problem, it is better to sketch the graph of two curves as follows
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Photo by Math Principles in Everyday Life |
Next, we need to get their point of intersection by solving the two systems of equations as follows
but
The above equation becomes
Using the second equation, the value of y is 2. Therefore, their point of intersection is (2, 2). Label further the figure as follows
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Photo by Math Principles in Everyday Life |
The slopes of two curves can be obtained by getting their derivative with respect to x as follows
for
then
for
but x = 2 from their point of intersection, therefore
The angle of intersection is given by the formula
Substitute the values of m1 and m2 to the above equation, we have
Therefore,
or