Question

The angle of intersection of the curve \( y = x^2 \), \( dy = 7 - x^2 \) at \( (1, 1) \) is:

• A. \( \frac{\pi}{2} \)
• B. \( \frac{\pi}{4} \)
• C. \( \frac{\pi}{3} \)
• D. \( \pi \)

Hint:

To find the angle of intersection between curves, use the formula involving their slopes at the point of intersection.

Answer 1

The Correct Option is A

The angle of intersection between the two curves can be determined using the formula for the angle between two curves: \[ \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| \] where \( m_1 \) and \( m_2 \) are the slopes of the tangents to the curves at the point of intersection. After calculation, the angle \( \theta = \frac{\pi}{2} \).