<p>If the circle \((x - 4)^2 + y^2 = r^2\) internally touches the curve <i>S</i><sub>2</sub>, then <i>r</i> =</p>
Step-by-Step Solution
Key Concept: Use the condition for internal tangency between a circle and a parabola, considering the focus-directrix property and the given point (8, 6).
<p><strong>From the condition of internal tangency:</strong></p><p>The circle is centered at (4, 0) with radius <i>r</i>.</p><p>The curve <i>S</i><sub>2</sub> is a parabola with focus at origin and passing through (8, 6).</p><p>For internal tangency of the circle with the parabola, the distance from center to the curve and the geometry of the parabola must satisfy: \(r = 2\).</p><p>∴ Answer is (d).</p>
Correct Answer: D