Question:
<p>Let P(1, 2) be a point from which pair of tangents are drawn to the ellipse <span class="math-tex">\(\frac{x^{2}}{4}\)</span> + y<sup>2</sup> = 1. Tangents touch the ellipse at points A and B. If the point of intersection of normals at points A and B is Q, then equation of PQ is:</p>
<p style="display:inline">2x + y = 4</p>
<p style="display:inline">3x - 2y + 1 = 0</p>
<p style="display:inline">2x - y = 0</p>
<p style="display:inline">3x + 2y = 7</p>
Step-by-Step Solution
Key Concept: The line PQ passes through the center of the ellipse when the coordinates of P(x1, y1) satisfy the condition a^2*x1^2 = b^2*y1^2, meaning the equation of PQ is simply the line joining P to the origin.
<p>2x - y = 0</p>
Correct Answer: C