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If θ denotes the acute angle between the curves, y = 10 − x² and y = 2 + x² at a point of their intersection, then |tan θ| is equal to:
- 4/9
- 8/15
- 7/17
- 8/17
Correct answer: 8/15
Solution
The acute angle between two curves at their intersection can be found using the slopes of the tangents to the curves at that point. By calculating the derivatives of both curves and using the formula for the tangent of the angle between two lines, we find that |tan θ| equals 8/15.
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