Question

The angle formed by the positive Y-axis and the tangent to \( y = x^2 + 4x - 17 \) at \( (2, -3) \) is:

• A. \( \tan^{-1} 9 \)
• B. \( \frac{\pi}{2} - \tan^{-1} 9 \)
• C. \( \frac{\pi}{3} \)
• D. \( \tan^{-1} 9 \)

Hint:

The angle between the Y-axis and a tangent line can be found using the slope of the tangent at a given point.

Answer 1

The Correct Option is B

The angle between the tangent and the Y-axis is given by the inverse tangent of the slope of the tangent. The slope of the tangent at \( (2, -3) \) is calculated by differentiating the equation \( y = x^2 + 4x - 17 \) and finding the slope at the point \( x = 2 \). After calculation, the angle is \( \frac{\pi}{2} - \tan^{-1} 9 \).