Question

find the angle between the curves r=a/1+cos theta and r=a/1-cos theta​

Answer 1

Final Answer: 180°

Given: r=a/1+cos theta and r=a/1-cos theta

To Find: The angle between the curves

Explanation:

1. The angle between two curves is the angle between their tangent lines at the point of intersection.

2. Both polar equations can be written in the form r=a/1+k cos theta and r=a/1-k cos theta.

3. The tangent lines at the point of intersection are given by y = mx + b where m = k and b = a/1+k or a/1-k.

4. The angle between two lines is given by arctan(m2-m1/1+(m1*m2))

5. Thus, the angle between the two curves is given by arctan(k/1+k2) = 180°.

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Answer 2

Answer: The angle between the curves r=a/1+cos theta and r=a/1-cos theta is 180 degrees.

To find this angle, we must first consider the equations.

The equation for the first curve

                                     r=a/1+cos theta

can be rearranged to be 1+cos theta = a/r, and the equation for the second curve

                                   r=a/1-cos theta

can be rearranged to be 1-cos theta = a/r.

We can observe that if cos theta = 1, then the two equations are equal and the angle between the curves is 0. On the other hand, if cos theta = -1, then the two equations are equal, and the angle between the curves is 180 degrees. Therefore, the angle between the curves r=a/1+cos theta and r=a/1-cos theta is 180 degrees.

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