Ellipse
Tangent and Chord Properties
Grade 11
Question:
<p>A vertical line passing through the point \((h, 0)\) intersects the ellipse \(\frac{x^2}{4} + \frac{y^2}{3} = 1\) at the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R. If \(D(h)\) = area of the triangle PQR, \(D_1 = \max_{1/2 \leq h \leq 1} D(h)\) and \(D_2 = \max_{1/2 \leq h \leq 1} D(h)\), then \(D_1 - 8D_2 = \) ?</p>
Step-by-Step Solution
Key Concept: Find the locus of intersection R of tangents at P and Q on the chord; express area as function of h; optimize to find Dā and Dā.
<p>Answer: 9</p>
Correct Answer: 9