Applications of Derivatives
Tangent to Curves
Grade 12
Question:
<p>The tangent at a point P on the curve \(y = \ln\left(\frac{2 + \sqrt{4 - x^2}}{2 - \sqrt{4 - x^2}}\right) - \sqrt{4 - x^2}\) meets the y-axis at T; then \(PT^2\) equals to:</p>
<p>(a) 2</p>
<p>(b) 4</p>
<p>(c) 8</p>
<p>(d) 16</p>
Step-by-Step Solution
Key Concept: Find the derivative to get the slope of tangent, then use point-slope form to find where it meets y-axis.
<p>To find $PT^2$, we need to find the tangent line at point P and its intersection with the y-axis at T, then calculate the distance.</p>
Correct Answer: c