Application of Derivatives
Angle of Intersection
Premium Question
Grade 12
Question:
If the curves $y = 2e^x$ and $y = ae^{-x}$ intersect orthogonally, then $a$ equals:
(1) $\frac{1}{2}$
(2) $2$
(3) $-\frac{1}{2}$
(4) $1$
Step-by-Step Solution
Key Concept: Find the slopes of both curves at their point of intersection, and use the orthogonality condition that the product of the two slopes equals $-1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)