Question

The angle of intersection of ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and circle \( x^2 + y^2 = ab \) is:

• A. \( \tan^{-1}\left( \frac{a + b}{ab} \right) \)
• B. \( \tan^{-1}\left( \frac{a - b}{ab} \right) \)
• C. \( \tan^{-1}\left( \frac{a + b}{\sqrt{ab}} \right) \)
• D. \( \tan^{-1}\left( \frac{a - b}{\sqrt{ab}} \right) \)

Hint:

When calculating the angle between two curves, find the derivatives at the point of intersection and use the formula for the tangent of the angle between two lines.

Answer 1

The Correct Option is B