Angle - Two Intersecting Curves

Category: Differential Calculus, Analytic Geometry, Algebra

"Published in Newark, California"

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

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

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

then

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