<p>Consider an ellipse \(\frac{x^2}{36} + \frac{y^2}{18} = 1\) and a hyperbola as described above. How many points in the x-y plane exist from where tangents can be drawn to the hyperbola?</p>
Step-by-Step Solution
Key Concept: Tangents to a hyperbola can be drawn from all points in the exterior region, which is an infinite set.
<p><strong>Solution:</strong> From any point outside the hyperbola, two real tangents can be drawn. From any point on the hyperbola, one tangent can be drawn (the tangent at that point). From points inside the hyperbola, no real tangents exist. Since the region outside the hyperbola contains infinitely many points, there are infinitely many points from which tangents can be drawn.</p><p>∴ Answer is (c).</p>
Correct Answer: c