Straight Lines
Regions and Inequalities
Grade 11
Question:
<p>If <i>d</i>(P, AB)² - <i>3/2</i> + <i>d</i>(P, AD)² ≥ 1, then area of region in which P lies is:</p>
<p>(a) 15 - 2π</p>
<p>(b) 10 - π/2</p>
<p>(c) 15 - π</p>
<p>(d) 15 - π/2</p>
Step-by-Step Solution
Key Concept: Recognize the quadratic inequality as defining an elliptical boundary; calculate area as total region minus ellipse area.
<p>The condition <i>d</i>(P, AB)² - 3/2 + <i>d</i>(P, AD)² ≥ 1 defines a region outside an ellipse in the coordinate system where AB and AD are the reference axes. The area of the region is calculated as the total rectangular area minus the elliptical area, yielding 15 - 2π.</p>
Correct Answer: a